Rational exponents & radicals

This course is a part of Mathematics I, a 16-course Topic series from Khan Academy.

Learn about expressions with rational exponents like x^(2/3), about radical expressions like √(2t^5), and about the relationship between these two forms of representation. Learn how to evaluate and simplify such expression.

This course contains 7 segments:

Exponent properties review

Practice using the exponent properties to rewrite powers, where the exponent is an integer that can either be positive or negative.

Radicals

Radicals (also known as roots) are a generalization of square roots. They are the inverse operation of any power. For example, the 5th root of 32 is 2, because 2⁵=32.

Rational exponents intro

Learn the definition for raising a number by a fractional exponent, like 8^⅔.

Properties of exponents (rational exponents)

In this tutorial you will rewrite variable expressions with rational exponents using the properties of exponents.

Advanced exponent & radical evaluation

Evaluate elaborate expressions that contain radicals and fractional exponents.

Simplifying square roots

We know how to evaluate square roots of perfect squares. For example, √16=4. What about the other square roots? It's harder to give an exact number, but we can simplify them so we have a better understanding of their value. For example, √32=4⋅√2. Learn more about it in this tutorial.

Simplifying radicals (higher-index roots)

Just like we can simplify square roots, we can simplify other radicals. This tutorial covers the simplification of higher-index roots. For example, ∜48=2⋅∜3.