GMAT Quantitative: Exponents and Roots

Question 1

Simplify: 2³ × 2⁵

Accepted Answer

2⁸

Answer

When multiplying powers with the same base, add the exponents: 2³ × 2⁵ = 2^(3+5) = 2⁸.

Question 2

Simplify: (3²)⁴

Accepted Answer

3⁸

Answer

Power of a power rule: (aᵐ)ⁿ = a^(m×n). (3²)⁴ = 3^(2×4) = 3⁸.

Question 3

What is the value of 5⁰?

Accepted Answer

1

Answer

Any nonzero number raised to the power 0 equals 1. 5⁰ = 1.

Question 4

What is the value of 2⁻³?

Accepted Answer

1/8

Answer

Negative exponent rule: a⁻ⁿ = 1/aⁿ. 2⁻³ = 1/2³ = 1/8.

Question 5

Simplify: 6⁸ ÷ 6³

Accepted Answer

6⁵

Answer

Division rule: aᵐ ÷ aⁿ = a^(m−n). 6⁸ ÷ 6³ = 6^(8−3) = 6⁵.

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