SAT Exponents and Radicals Practice Flashcards

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

Answer: 5 × 10¹

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

Simplify: (x³)^(2/3)

Answer: x²

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

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

Answer: 1

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

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

Answer: 200 × 3^(t/4)

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

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

Answer: 3x²y

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

Solve for x: 4^x = 8

Answer: x = 3/2

4^x = 2^(2x) and 8 = 2³. So 2x = 3, x = 3/2.

Simplify: (16)^(3/4)

Answer: 8

16^(3/4) = (⁴√16)³ = 2³ = 8.