PSAT Math Multiple-Choice Question 111: Answer and Explanation

Question: 111

If the equation above, where k is a constant, is true for all positive values of a and b, what is the value of k?

• A. 3
• B. 4
• C. 7
• D. 10

Correct Answer: C

Explanation:

C

The question asks for the value of a constant that appears as part of a fractional exponent. When dealing with questions about exponents, remember the MADSPM rules. The MA part of the acronym indicates that Multiplying matching bases means to Add the exponents. The PM part of the acronym indicates that raising a base with an exponent to another Power means to Multiply the exponents. Use the order of operations to apply the exponents outside the parentheses to the bases inside by multiplying the exponents to get . Although it is possible to reduce some of these exponents, the next step will be to add them together, since the bases are multiplied. Leave the exponents in fractional form to make that easier, getting . According to the equation, this is equal to , so k must equal 7. The correct answer is (C).