Bluebook SAT Test SAT Exponents and Radicals Practice 4

Question 1

Which expression is equivalent to (x^4)^(1/2) × x^(−2)?

Accepted Answer

1

Answer

(x⁴)^(1/2) = x² and x^(−2) = 1/x². Product = x² · x^(−2) = x⁰ = 1.

Question 2

The half-life of a radioactive element is 10 years. Starting with 640 grams, how many grams remain after 40 years?

Accepted Answer

40

Answer

40 years = 4 half-lives. Remaining = 640 × (1/2)⁴ = 640/16 = 40 grams.

Question 3

Which of the following equals 2^50 × 4^25?

Accepted Answer

2^100

Answer

4^25 = (2²)^25 = 2^50. So 2^50 × 2^50 = 2^100.

Question 4

Solve: √(3x + 1) = 4

Accepted Answer

x = 5

Answer

Square both sides: 3x + 1 = 16 → x = 5.

Question 5

What is the product (2√6)(3√10)?

Accepted Answer

12√15

Answer

(2)(3)√(6×10) = 6√60 = 6·2√15 = 12√15.

Bluebook SAT Practice Test