# Power Functions and Exponents

In this document, we discuss power functions and how exponents affect them.

### Introduction

Power functions use rational numbers as exponents. There are several properties that define their behavior. We will go over these properties in some example problems.

### Example 1

Simplify $$16^3/4$$

$\left( \frac{1}{t}\right)^{\!3/2}$

You can look at this as saying the 4th root of 16 cubed.

$\sqrt[4]{16^3}$

The fourth root of 16 = 2.

$(2)^3 = 8$

### Example 2

Simplify: $$\left \frac{4^ \right {\!⅓}} {4^ \right {\!⅚}}$$

Put the numerator and denominator into one term and subtract the exponents.

$= \left 4^{\right {\!⅓ - \!⅚} }$

Subtract the exponents.

$= \left 4^{\right {\!-½}}$

A negative exponent is just an inverse root. Let us move it to the denominator.

$= \frac{ 1}{\sqrt{4}}$

Now, just simplify.

$= \frac{1}{2}$

This article was updated on July 21, 2022