Title: Unit 11 Quiz
Course: Technical Math for Industry

Q: Evaluate: when
- 512 (Correct.)
- 32 (Incorrect. This expression is equal to . It appears that you calculated the exponent before doing the multiplication inside the parentheses. The correct order of operations is to do calculations inside parentheses before exponents.)
- 128 (Incorrect. This is the value of , and you should be finding the value of . That is, you should multiply and then evaluate the exponent.)
- 24 (Incorrect. You may have correctly substituted and multiplied first: . However, it seems that you multiplied by 3 rather than using it as an exponent.)
A: 512

Q: Evaluate: if and
- 8 (Incorrect. You may have switched the values of x and y when you were substituting into the expression. You also may have evaluated the first term incorrectly. You need to apply the exponent and then multiply, not the other way around.)
- 9 (Incorrect. You may have used the incorrect order of operations when computing . You need to apply the exponent and then multiply, not the other way around.)
- 12 (Correct.)
- 11 (Incorrect. You may have switched the values of x and y when you were substituting into the expression. You should be calculating .)
A: 12

Q: Evaluate when .
- 1,024 (Incorrect. It seems that you overlooked the negative in the exponent. The second factor is equal to which is)
- 64 (Correct.)
A: 64
If wrong: Incorrect. You may have reversed the signs of the exponents. This answer would be correct if the given expression were . The actual expression is equal to .
If wrong: Incorrect. This is the result of an incorrect order of operations. The negative in the second exponent does not apply to the factor .

Q: Simplify:
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. The product rule says that to multiply factors with like bases you add the exponents. You may have done that with the variable factors, but you also added the exponent of the constant 5 to the other exponents. The numbers 5 and c are unlike bases. Also, the factor 5 should only have an exponent of 1, but since it is inside the parentheses, the exponent 10 is being applied to it too.
If wrong: Incorrect. Even though this is a multiplication problem, you do not multiply the exponents. Apply the product rule, which says . That is, to multiply factors with like bases, you add the exponents. For this problem, you will have to use this rule twice.
If wrong: Incorrect. The product rule says that to multiply factors with like bases you add the exponents. You may have done that with the variable factors, but you also added the exponent of the constant 5 to the other exponents. The numbers 5 and c are unlike bases.

Q: Simplify:
A: (a choice with no text)
If wrong: Incorrect. You have used the wrong order of operations. This would have been the answer if the problem was to simplify . You have to apply exponents before multiplication. So in the original expression you should simplify first, and then use the product rule.
If wrong: Incorrect. You have used the wrong order of operations. This would have been the answer if the problem was to simplify . You have to apply exponents before multiplication. So in the original expression you should simplify first, and then use the product rule.
If wrong: Incorrect. You probably forgot that , and treated this factor as if the exponent was 0. Use the power rule first to simplify , and then use the product rule.
If right: Correct.

Q: Simplify:
A: (a choice with no text)
If wrong: Incorrect. You may have correctly canceled common factors and used the quotient rule to simplify this expression, but forgot that a negative divided by a negative is a positive.
If wrong: Incorrect. You may have correctly canceled common factors, but made a mistake using the quotient rule. You can rewrite as a fraction with a positive exponent.
If wrong: Incorrect. You may have correctly canceled common factors and used the quotient rule to simplify this expression to , but then mistakenly replaced with . A negative exponent does not give you a negative sign. You can rewrite as a fraction with a positive exponent.
If right: Correct.

Q: Simplify:
A: (a choice with no text)
If wrong: Incorrect. While correctly multiplying exponents to simplify to you may have mistakenly multiplied exponents to simplify . The product rule tells you to add these exponents.
If wrong: Incorrect. While correctly adding exponents to simplify to you may have mistakenly added exponents to simplify . The power rule tells you to multiply these exponents.
If right: Correct.
If wrong: Incorrect. You may have correctly applied all the rules of exponents but forgot that a negative divided by a negative is a positive.

Q: Simplify the expression.
A: (a choice with no text)
If wrong: Incorrect. You need to raise every factor inside the parentheses to the power outside. You raised the variable factors to the fifth power, but you forgot to raise the constant to the fifth power.
If right: Correct. Apply the exponent 5 to each factor within the parentheses: Simplify, using the Power Rule:
If wrong: Incorrect. Raising a negative number to an odd power means that you are multiplying an odd number of negative numbers. So the result will be negative.
If wrong: Incorrect. When you applied the exponent 5 to the factors and , you added the exponents instead of multiplying them.

Q: Simplify the expression:
A: (a choice with no text)
If wrong: Incorrect. You probably correctly applied the exponent 3 to the variable factors, used the power rule, and used the quotient rule. However, you should also have applied the exponent to the constant factor, .
If right: Correct. Apply the exponent 3 to each factor individually: Simplify and use the power rule: Use the quotient rule:
If wrong: Incorrect. A negative number raised to the third power is the same as the product of three negative numbers. The product of an odd number of negatives is negative. So is negative.
If wrong: Incorrect. You may have added the exponent 3 to the exponent of each variable factor instead of multiplying by it, and then used the quotient rule.

Q: Simplify the expression.
A: (a choice with no text)
If wrong: Incorrect. When multiplying and , you multiplied the exponents together instead of adding them.
If wrong: Incorrect. You probably applied the exponent 2 to only the last factor inside the parentheses, . You should apply it to every factor inside the parentheses.
If wrong: Incorrect. You probably applied the exponent 2 to the variable factors and correctly used the power and product rules. However, you forgot to apply the exponent 2 to the constant 4.
If right: Correct. Apply the exponent 2 to each factor in the first expression: Calculate and use the Power Rule to square : Multiply the coefficients and use the Product Rule:

Q: Express 0.000000018 in scientific notation.
A: (a choice with no text)
If wrong: Incorrect. You knew the answer should have a negative exponent since the decimal point was moved to the right. But you may have counted the number of zeros to find the exponent. Instead, you should count the number of places the decimal point was moved.
If wrong: Incorrect. Although is equivalent to 0.000000018, it is not written in scientific notation, because 18 is not between 1 and 10.
If wrong: Incorrect. You may not have seen that the exponent in this choice is positive. Since you moved the decimal point to the right, the scientific notation should have a negative exponent.
If right: Correct. Move the decimal point to the right until you get a number between 1 and 10. For the given number this would be 1.8. Since the decimal point was moved eight places to the right, you multiply the decimal by 10 raised to a negative power.

Q: Multiply, expressing the product in scientific notation.
A: (a choice with no text)
If wrong: Incorrect. You may have correctly regrouped the factors and found the product of the numbers. However, when multiplying the powers of 10 you subtracted 16 from instead of adding and 16.
If wrong: Incorrect. This is the correct product, but it is not in scientific notation, because 50.38 is larger than 10.
If wrong: Incorrect. You probably found the correct product , but when converting 50.38 to scientific notation, you incorrectly wrote it as , instead of .
If right: Correct. Regroup the factors: Multiply the numbers: Use the product rule: Convert 50.38 into scientific notation: Regroup and use the product rule:

Q: The diameter of a hydrogen atom is about meter. Suppose hydrogen atoms were arranged side by side in a straight line. Multiply these numbers to find the length of this line of atoms. What is the length in scientific notation?
- meter (Incorrect. This is the correct product, but it is not expressed in scientific notation, because 42 is not between 1 and 10.)
- meter (Correct. Regroup the factors and multiply the numbers: Use the product rule: Convert 42 to , regroup, and multiply:)
- meter (Incorrect. This is the correct product, but it is not expressed in scientific notation, because 0.042 is less than 1 and there is no multiplication by a power of 10.)
- meter (Incorrect. You probably multiplied the numbers and the powers of 10 correctly, but when you converted 42 to you forgot to regroup the powers of 10 and find .)
A: meter

Q: What are the exponent and coefficient of the expression ?
- The exponent is 1 and the coefficient is 5. (Incorrect. The exponent is the power that the variable is raised to. If a variable has no exponent, that is the same as having an exponent of 1. The coefficient is the numerical factor of the term. The constant factor is not 5.)
- The exponent is 1 and the coefficient is . (Correct. The exponent is the power that the variable is raised to. If a variable has no exponent, that is the same as having an exponent of 1. The coefficient is the numerical factor of the term.)
- The exponent is 0 and the coefficient is 5. (Incorrect. The exponent is the power that the variable is raised to. Remember that if a variable has no exponent, that is the same as having an exponent of 1. The coefficient is the numerical factor of the term. The constant factor is not 5.)
- The exponent is 0 and the coefficient is . (Incorrect. The exponent is the power that the variable is raised to. Remember that if a variable has no exponent, that is the same as having an exponent of 1. The coefficient is the numerical factor of the term.)
A: The exponent is 1 and the coefficient is .

Q: Evaluate for .
- 32 (Incorrect. While calculating , you may have thought that was positive. Remember to evaluate exponents before multiplication.)
- 8 (Correct. Since , the polynomial equals .)
- 0 (Incorrect. While calculating , you may have thought that was negative and that was positive. Remember to evaluate exponents before multiplication.)
A: 8
If wrong: Incorrect. You may have substituted 2 for x instead of . You need to find the value of .

Q: Simplify .
A: (a choice with no text)
If wrong: Incorrect. You may have incorrectly simplified the term . The correct order of operations is to apply the exponent first and then multiply, so .
If wrong: Incorrect. You may have thought that you could combine unlike terms by adding coefficients. You can only combine terms with the same variable and exponent. The given polynomial equals , and you need to combine the like terms in the parentheses.
If right: Correct. First identify the like terms. Then combine them by adding coefficients. Remember that .
If wrong: Incorrect. You may have thought that you could combine unlike terms by adding exponents. When you multiply you add exponents. When you add or subtract, you can only combine terms with the same variable and exponent. The given polynomial equals , and you need to combine the like terms in the parentheses.

Q: Find the sum:
A: (a choice with no text)
If wrong: Incorrect. You incorrectly tried to combine and , but these are unlike terms and cannot be combined. Regroup and combine like terms to find the sum.
If right: Correct. Rewrite subtraction as addition of the opposite: Regroup: Combine like terms:
If wrong: Incorrect. You ignored the minus signs when adding. You need to rewrite the problem as before regrouping and combining like terms.
If wrong: Incorrect. You incorrectly tried to combine and , as well as 8 and , but these are unlike terms and cannot be combined. Regroup and combine like terms to find the sum.

Q: Find the opposite of .
A: (a choice with no text)
If right: Correct. Multiply the polynomial by : Distribute to each term in the polynomial: Multiply each coefficient by : Rewrite addition of a negative term as subtraction:
If wrong: Incorrect. You changed the sign of the negative term, but each term in the polynomial must have its sign changed.
If wrong: Incorrect. You changed the sign of only the positive terms, but each term in the polynomial must have its sign changed.
If wrong: Incorrect. You changed the sign of only the first term in the polynomial, but each term must have its sign changed.

Q: Subtract.
A: (a choice with no text)
If wrong: Incorrect. After changing subtraction to addition of the opposite, you incorrectly tried to combine and , but these are unlike terms and cannot be combined. Make sure to match like terms when regrouping.
If wrong: Incorrect. You may have forgotten to change the sign of in the second polynomial when changing subtraction to addition of the opposite.
If wrong: Incorrect. You added the polynomials instead of subtracting. You should change subtraction to adding the opposite and find .
If right: Correct. Change subtraction to addition of the opposite: Regroup to match like terms: Combine like terms:

Q: Multiply.
A: (a choice with no text)
If right: Correct. In order to multiply monomials, multiply the coefficients and add the exponents.
If wrong: Incorrect. It appears that you added the coefficients. In order to multiply monomials, you must multiply the coefficients and add the exponents.
If wrong: Incorrect. It appears that you added the coefficients and multiplied the exponents. In order to multiply monomials, you must multiply the coefficients and add the exponents. Also, remember that a variable with no exponent is the same as a variable with an exponent of 1.
If wrong: Incorrect. It appears that you multiplied the exponents or ignored the exponent on the first monomial. Remember that a variable with no exponent is the same as a variable with an exponent of 1. In order to multiply monomials, you must multiply the coefficients and add the exponents.

Q: Simplify .
A: (a choice with no text)
If right: Correct. To multiply a polynomial by a monomial, distribute the monomial to each of the terms in the polynomial. Remember to multiply coefficients and add exponents.
If wrong: Incorrect. You must distribute the negative sign on the outside to every term of the polynomial. It was distributed only to the first term.
If wrong: Incorrect. To multiply a polynomial by a monomial, distribute the monomial to every term of the polynomial. It appears that you distributed -x^2 only to the first term of the polynomial.
If wrong: Incorrect. First, you must distribute the negative sign on the outside to every term of the polynomial. It was distributed only to the first term. Second, you must remember that x is the same as x1 and that when you multiply monomials you must add the exponents.

Q: Find the product of .
A: (a choice with no text)
If wrong: Incorrect. You may have correctly used FOIL, but then combined the middle terms incorrectly. If you are adding and , you must apply the same rules you learned for adding positive and negative numbers.
If right: Correct. Using the FOIL method, you find:
If wrong: Incorrect. Multiply each term in the first binomial with each term in the second binomial, and then combine the two like terms. It appears that you multiplied the first two terms and the last two terms, but and are missing.
If wrong: Incorrect. It appears that you may have added the coefficients. Instead, you need to multiply each term in the first binomial with each term in the second binomial, and then combine the two like terms. FOIL is an easy way to remember that.

Q: Multiply:
A: (a choice with no text)
If wrong: Incorrect. It appears that you ignored the negative sign on the 1. When you are multiplying individual terms, make sure that you carefully multiply the coefficients and find the right sign for each term.
If wrong: Incorrect. It appears that you did not distribute each term in the binomial to each term in the trinomial. Always multiply each term in the first polynomial with each term in the second polynomial.
If right: Correct.
If wrong: Incorrect. It appears that you added the two polynomials together rather than multiplying them. Multiply each term in the first polynomial with each term in the second polynomial and then combine the like terms.

Q: Square the binomial:
A: (a choice with no text)
If wrong: Incorrect. You left out the middle term. To square a binomial, you can use . In this case, and .
If right: Correct. . In this case, and , so .
If wrong: Incorrect. You have simply doubled each term. To square the binomial, you can use . In this case, and .
If wrong: Incorrect. You correctly squared each term, but the middle term, , is not correct. To square a binomial, you can use . In this case, and .

Q: Find the product:
A: (a choice with no text)
If wrong: Incorrect. You may have been thinking of the square of a binomial. To find this type of product, you can use . Note that there is no middle term in the result. In this case and .
If wrong: Incorrect. It appears that you doubled the terms instead of squaring them. To find this type of product, you can use . In this case and .
If right: Correct. To find the product, you can use . In this case and , so .
If wrong: Incorrect. It appears that you added the coefficients of the first terms instead of squaring them. To find this type of product, you can use . In this case and .

Q: Divide:
A: (a choice with no text)
If wrong: Incorrect. When dividing monomials, divide the coefficients and divide the variables by subtracting the exponents. It appears that you reversed the numerator and denominator. If you divide and get a negative exponent, rewrite that factor, and only that factor, in the denominator with a positive exponent.
If right: Correct.
If wrong: Incorrect. When dividing the variables, you may have subtracted the exponents incorrectly or been confused about where the variable factor should end up. If you divide and get a negative exponent, rewrite that factor in the denominator with a positive exponent.
If wrong: Incorrect. It appears that you divided the coefficients correctly, but made a mistake when dividing the variables. Because the x in the numerator did not have an exponent, you may have treated it as if the exponent was 0. Remember that when there is no exponent, that is the same as an exponent of 1.

Q: Divide:
A: (a choice with no text)
If wrong: Incorrect. Divide each term in the polynomial by the monomial. It appears that you divided 15 by 5 instead of 5 by 15 in the first term.
If wrong: Incorrect. Divide each term in the polynomial by the monomial. It appears that you divided only the middle term of the polynomial by the monomial.
If wrong: Incorrect. Divide each term in the polynomial by the monomial. It appears that you divided only the first term of the polynomial by the monomial.
If right: Correct. Divide each term in the polynomial by the monomial.

Q: Divide:
A: (a choice with no text)
If wrong: Incorrect. During the first stage of the division process, when you should have subtracted , you may have added and . This would have given you left over for the next stage, when you should have had . Make sure that you distribute the minus sign when you get to the steps involving subtraction.
If wrong: Incorrect. It appears that you may have done the division process correctly up until the last step. At that point you should have subtracted , but you may have added and instead. Make sure that you distribute the minus sign when you get to the steps involving subtraction.
If right: Correct.
If wrong: Incorrect. During the first stage of the division process, when you should have subtracted , you may have added and . Then during the second stage you made a similar error in subtraction. Make sure that you distribute the minus sign when you get to the steps involving subtraction.

Q: Divide.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. During the first stage of the division process you should have subtracted from the dividend. While subtracting , you may have added the terms to the dividend. Make sure that you distribute the minus sign when you get to the steps involving subtraction.
If wrong: Incorrect. During the first stage of the division process you should have subtracted from the dividend. While subtracting , you may have added the terms to the dividend. Then you made a similar mistake when you got to the next subtraction. Make sure that you distribute the minus sign when you get to the steps involving subtraction.
If wrong: Incorrect. It appears that you correctly applied the division process up until the last step. At that point you should have subtracted . You may have added the terms to . Make sure that you distribute the minus sign when you get to the steps involving subtraction.

Q: Evaluate the expression for and .
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. You may have reversed the variables when substituting their values into the expression. should be substituted in for both a's and 4 should be substituted in for b, to give you .
If wrong: Incorrect. You may have incorrectly evaluated as instead of 9.
If wrong: Incorrect. You may have evaluated the expression in order from left to right. Remember to follow the correct order of operations by multiplying before adding.

Q: Simplify:
A: (a choice with no text)
If right: Correct. To simplify an expression, reorder the addends and combine like terms.
If wrong: Incorrect. It appears that you added the correct like terms, but then added exponents as well. Exponents are not added when combining like terms.
If wrong: Incorrect. It appears as if you combined all terms together and added exponents as well. Only like terms can be combined and the exponents will not change.
If wrong: Incorrect. It appears that you added the coefficients of the like terms, ignoring that some of the coefficients were negative. When you combine like terms and add their coefficients, make sure you use the rules you learned for adding positive and negative numbers.

Q: Add:
A: (a choice with no text)
If wrong: Incorrect. You appear to have added all coefficients to make one term. When adding polynomials, be sure to combine only like terms.
If wrong: Incorrect. You correctly added the coefficients of the like terms, but you also added their exponents. When you combine like terms, their exponents do not change.
If wrong: Incorrect. It appears that you added the first terms to each other and second terms to each other, even though they are not like terms. When adding polynomials, be sure to combine only like terms.
If right: Correct. Remove the parentheses, rewrite subtraction as addition of the opposite, reorder, and combine like terms.

Q: Subtract.
A: (a choice with no text)
If wrong: Incorrect. It appears that you inconsistently applied the minus sign to some terms in the second polynomial and not to others. When you subtract polynomials you should remove the parentheses and change the signs of all the terms of the second polynomial. Then combine the like terms.
If wrong: Incorrect. It appears that you subtracted the first polynomial from the second polynomial. Perhaps you reversed them when lining them up vertically. To subtract polynomials, remove the parentheses, change the signs of the terms of the second polynomial, regroup, and then combine like terms.
If wrong: Incorrect. It appears that you added the polynomials instead of subtracting them. To subtract polynomials, remove the parentheses, change the signs of the terms of the second polynomial, regroup, and then combine like terms.
If right: Correct. Remove the parentheses and change the signs of the terms of the second polynomial: Regroup and combine like terms:

Q: Multiply:
A: (a choice with no text)
If wrong: Incorrect. It appears that you distributed correctly, but then combined the middle terms by adding exponents. Terms cannot be combined this way. You can only combine like terms.
If wrong: Incorrect. It appears that you used FOIL, but added instead of multiplying coefficients for each product.
If wrong: Incorrect. It appears that you used FOIL, but multiplied instead of adding exponents for each product.
If right: Correct. Use FOIL to multiply two binomials. FIRST: OUTER: INNER: LAST: Add. Combine like terms, if any:

Q: Divide:
A: (a choice with no text)
If wrong: Incorrect. You divided only the first term in the numerator by the denominator. To divide a polynomial by a monomial, divide each term separately by the denominator.
If wrong: Incorrect. You seem to have added the exponents. When you divide variables, the exponents of the same variable are subtracted, not added.
If wrong: Incorrect. It appears that you subtracted the coefficients. When you divide variables, the exponents of the same variable can be subtracted. However, you should just do ordinary division with the coefficients.
If right: Correct. To divide a polynomial by a monomial, divide each term separately by the denominator.