PSAT Math Multiple-Choice Question 11: Answer and Explanation

Question: 11

Which of the following values of b makes the equation above true?

• A. 4
• B. 6
• C. 8
• D. 12

Correct Answer: D

Explanation:

D

The question asks for the value of a variable in an equation that includes fractional exponents. Simplify this equation one piece at a time and solve for b. Start with the left side. Take the cube root of 64 and rewrite: . Taking the cube root is the same as raising an expression to the power, so continue simplifying the left side: . Use the MADSPM rules to multiply the exponents: . Now that the left side is simplified, start simplifying the right side. Be careful as you square each term in the parentheses: . Continue simplifying the right side of the equation to get 16 × 3 × a² = 48a². At this point, . When dealing with exponents, equal terms that have the same bases also have equal exponents, so set the terms with base a equal to each other to solve for the value of b: . Solve for b by setting the exponents equal to each other: . Multiply both sides by 6 to get b = 12. An alternative final step is to set 48 equal to 4b and get b = 12. The correct answer is (D).