SSAT Math Question 221: Answer and Explanation

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Question: 221

5. If (x^a)³ = x¹⁵ and = x⁷, then b -a =

A. –4
B. –2
C. 2
D. 4

Correct Answer: D

Explanation:

The answer is D

Solve for the variables by applying the rules of exponents. When an exponential expression is raised to another power, multiply the exponents. Therefore, (x^a)³ = x³^a = x¹⁵. Therefore, 3a = 15, and a = 5. When exponential expressions with like bases are divided, subtract the exponents. Therefore, = x^b^-2 = x⁷. Therefore, b - 2 = 7, and b = 9. 9 - 5 = 4.

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