PSAT Math Multiple-Choice Question 101: Answer and Explanation

Question: 101

If the expression above is true for all values of x where x > 0, what is the value of b?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

The question asks for the value of b in an equation with exponents. When dealing with questions about exponents, remember the MADSPM rules. The DS part of the acronym indicates that Dividing matching bases means to Subtract the exponents. The bases on the left of the equation do not match, so use fractional exponents to simplify the equation. Radicals can be turned into fractional exponents by the rule power over root. Convert the radicals to fractional exponents to get . Next, subtract the exponents to get . Multiply the numerator and the denominator of the first fraction by 2 to get a common denominator of 4 on the exponents. The equation becomes , which is . The bases are the same, so the exponents must be equal. Therefore, b = . The correct answer is (C).