Bluebook SAT Test SAT Exponents and Radicals Practice 3

Question 1

Which of the following is equivalent to x^(−3)?

Accepted Answer

1/x³

Answer

A negative exponent means the reciprocal: x^(−3) = 1/x³.

Question 2

If 3^m = 81 and 3^n = 27, what is m − n?

Accepted Answer

1

Answer

3^m = 3^4 → m = 4; 3^n = 3^3 → n = 3. m − n = 1.

Question 3

Rationalize the denominator: 6/√3

Accepted Answer

2√3

Answer

6/√3 × (√3/√3) = 6√3/3 = 2√3.

Question 4

A quantity grows according to y = 500 × 2^(t/5). What is y when t = 15?

Accepted Answer

4,000

Answer

y = 500 × 2^(15/5) = 500 × 2³ = 500 × 8 = 4,000.

Question 5

Simplify: (a²b⁻³)/(a⁻¹b²)

Accepted Answer

a³/b⁵

Answer

Subtract exponents: a^(2−(−1)) × b^(−3−2) = a³b^(−5) = a³/b⁵.

Bluebook SAT Practice Test