PSAT Math Multiple-Choice Question 9: Answer and Explanation

Question: 9

If x = 8x, which of the following could be the value of x?

• A. 2
• B. 4
• C. 6
• D. 8

Correct Answer: B

Explanation:

B

The question asks for the value of a variable in an equation involving a fractional exponent. When dealing with a question about fractional exponents, remember the exponent rules: in a fractional exponent, the numerator is the power the base is raised to and the denominator is the root of the base. Therefore, can be written as , so = 8x. Solve for x. To begin to isolate x, square both sides of the equation to get x⁵ = 64x². Divide by x² on each side. Remember the MADSPM rules: the DS part of the MADSPM acronym indicates that Dividing matching bases means to Subtract the exponents. So, , and x³ = 64. Take the cube root of both sides to get x = 4. The correct answer is (B).