SAT Practice Questions: Working with Exponents

Practice questions

1. In this equation, what is the value of x – y?
   
   A. 2 B. 3 C. 4 D. 5
2. What is the value of a in the equation if b² = 5 and a < 0?
   
   A. –1 B. –2 C. –3 D. –4

Answers and explanations

1. The correct answer is Choice (C). Start with the fraction and subtract the exponents, just as you'd do to divide any other terms with like bases:
   
   You know that 16 equals 2⁴, so set 2⁴ equal to the 2 with the subtracted exponents: 2^x–y = 2⁴ Therefore x – y = 4.
2. The correct answer is Choice (C). Simplify the exponential expression by multiplying the exponents, just as you'd do for any other base with an exponent of an exponent:
   
   You know that 16 equals 2⁴, so set 2⁴ equal to the 2 with the subtracted exponents:
   
   Therefore, a² – b² = 4. You know that b² = 5, so plug in the value of b²:
   
   You also know that a < 0, so a has to be –3.