Bluebook SAT Test SAT Exponents and Radicals Practice 7

Question 1

What is (2.5 × 10⁸) ÷ (5.0 × 10³) in scientific notation?

Accepted Answer

5.0 × 10⁴

Answer

(2.5 ÷ 5.0) × 10^(8−3) = 0.5 × 10⁵ = 5.0 × 10⁴.

Question 2

If f(x) = x^(2/3) and f(k) = 4, what is k?

Accepted Answer

8

Answer

k^(2/3) = 4 → k = 4^(3/2) = (√4)³ = 8.

Question 3

Which is greater: 2^30 or 3^20?

Accepted Answer

3^20

Answer

2^30 = (2³)^10 = 8^10 and 3^20 = (3²)^10 = 9^10. Since 9 > 8, we have 3^20 > 2^30.

Question 4

Simplify √(x² + 6x + 9) for x ≥ 0.

Accepted Answer

x + 3

Answer

x² + 6x + 9 = (x+3)². For x ≥ 0, x+3 > 0, so √((x+3)²) = x+3.

Question 5

What is the simplified form of (27/8)^(2/3)?

Accepted Answer

9/4

Answer

(27/8)^(2/3) = (∛(27/8))² = (3/2)² = 9/4.

Bluebook SAT Practice Test