# Lesson 5

Negative Rational Exponents

- Let’s investigate negative exponents.

### Problem 1

Write each expression in the form \(a^b\), without using any radicals.

- \(\sqrt{5^9}\)
- \(\frac{1}{\sqrt[3]{12}}\)

### Problem 2

Write \(32^{\text-\frac25}\) without using exponents or radicals.

### Problem 3

Match the equivalent expressions.

### Problem 4

Complete the table. Use powers of 27 in the top row and radicals or rational numbers in the bottom row.

\(27^1\) | \(27^{\frac13}\) | \(27^{\text- \frac12}\) | |||

27 | \(\sqrt{27}\) | 1 | \(\frac13\) |

### Problem 5

What are the solutions to the equation \((x-1)(x+2)=\text-2\)?

### Problem 6

Use exponent rules to explain why \((\sqrt{5})^3 = \sqrt{5^3}\).