ASVAB Mathematics Knowledge Practice: Exponents

When you run into exponent problems on the Mathematics Knowledge subtest on the ASVAB, they may look a little complicated. As you'll see in the following practice questions, though, if you know the different exponent rules, they're quite easy to solve.

Practice questions

1. Simplify: (3x⁷y⁵)² A. 9x⁷y⁵ B. 9x¹⁴y⁵ C. 9x⁷y¹⁰ D. 9x¹⁴y¹⁰
2. Simplify: ((x⁵)⁷)⁹ A. x²¹ B. x²² C. x³¹ D. x³¹⁵

Answers and explanations

1. The correct answer is Choice (D).

   To simplify expressions that contain exponents, raise everything in the parentheses by the exponent outside the parentheses. Technically, you'll apply the exponent rule, which says (ab)ⁿ = aⁿbⁿ. In this case,

   

2. The correct answer is Choice (D).

   Apply the exponent rule, which says

   

   Multiply the exponents, beginning with the innermost parentheses:

   

   Move on to the outer exponent: