Bluebook SAT Test SAT Exponents and Radicals Practice

Question 1

Which of the following is equivalent to x^(2/3)?

Accepted Answer

∛(x²)

Answer

The rational exponent 2/3 means the cube root of x squared: x^(2/3) = ∛(x²).

Question 2

Simplify: (3x²y³)² × (2xy)³

Accepted Answer

72x⁷y⁹

Answer

(3x²y³)² = 9x⁴y⁶ and (2xy)³ = 8x³y³. Product = 72x^(4+3)y^(6+3) = 72x⁷y⁹.

Question 3

What is the value of 27^(−2/3)?

Accepted Answer

1/9

Answer

27^(2/3) = (∛27)² = 3² = 9. The negative exponent gives the reciprocal: 1/9.

Question 4

If 2^x = 32, what is the value of 2^(x−3)?

Accepted Answer

4

Answer

2^x = 2^5 so x = 5. Then 2^(5−3) = 2² = 4.

Question 5

Simplify: √(50x⁴y²)

Accepted Answer

5x²y√2

Answer

√(50x⁴y²) = √(25·2·x⁴·y²) = 5x²y√2.

Bluebook SAT Practice Test