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.)