SAT Topic 4

Exponents & radicals

Laws of exponents, fractional and negative exponents, simplifying radicals.

Concept

Memorise these. They show up everywhere:

To simplify a radical like √72, factor the radicand and pull out perfect squares: √72 = √(36·2) = 6√2.

Worked example 1

Simplify (2x³)² · x⁻⁴.

Solution
Power. (2x³)² = 4x⁶
Combine. 4x⁶ · x⁻⁴ = 4x^(6 − 4) = 4x²
4x²

Worked example 2

Simplify √72.

Solution
Factor. 72 = 36 · 2, and 36 is a perfect square.
Split. √72 = √36 · √2 = 6√2
6√2

Practice test

8 questions on exponent laws, fractional/negative exponents, scientific notation, and simplifying radicals.

Practice test · 8 questions Question 1 of 8 · Score 0