Concept 2

Use properties of exponents and radicals (including rational exponents).

Use exponent rules and rational exponents correctly, including roots and powers.

Core Idea

Use exponent rules deliberately: same base means combine exponents correctly, and a rational exponent tells you both a root and a power.

Understanding

Rule: Rational exponents and radicals are two forms of the same idea.

In $𝑎 𝑚 𝑛$ , the denominator $𝑛$ tells you the root and the numerator $𝑚$ tells you the power. On ACT questions, the trap is often procedural: students square when they should take a root first, or they distribute exponents incorrectly across addition instead of across multiplication.

Question

Worked Example

What is the value of $2723$ ?

Select an answer to see the explanation