# Lesson 5

Negative Rational Exponents

• Let’s investigate negative exponents.

### Problem 1

Write each expression in the form $$a^b$$, without using any radicals.

1. $$\sqrt{5^9}$$
2. $$\frac{1}{\sqrt[3]{12}}$$

### 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 $$\frac13$$
(From Unit 3, Lesson 3.)

### Problem 5

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

(From Unit 2, Lesson 11.)

### Problem 6

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

(From Unit 3, Lesson 4.)