Bluebook SAT Test SAT Exponents and Radicals Practice 2

Question 1

If a = 3 × 10⁵ and b = 6 × 10³, what is a/b expressed in scientific notation?

Accepted Answer

5 × 10¹

Answer

a/b = (3/6) × 10^(5−3) = 0.5 × 10² = 5 × 10¹.

Question 2

Simplify: (x³)^(2/3)

Accepted Answer

x²

Answer

(x³)^(2/3) = x^(3 × 2/3) = x² by the power-of-a-power rule.

Question 3

Which of the following equals (√3 + √2)(√3 − √2)?

Accepted Answer

1

Answer

Using difference of squares: (√3)² − (√2)² = 3 − 2 = 1.

Question 4

A bacteria colony triples every 4 hours. Starting with 200 bacteria, which expression gives the count after t hours?

Accepted Answer

200 × 3^(t/4)

Answer

The count triples every 4 hours, so the formula is 200 × 3^(t/4).

Question 5

What is the simplified form of ∛(27x⁶y³)?

Accepted Answer

3x²y

Answer

∛(27x⁶y³) = ∛27 × ∛(x⁶) × ∛(y³) = 3 × x² × y = 3x²y.

Bluebook SAT Practice Test