Lesson 5

Negative Rational Exponents

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Problem 1

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

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

Solution

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Problem 2

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

Solution

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Problem 3

Match the equivalent expressions.

A:

\(8^{\frac13}\)

B:

\(8^{\text- \frac13}\)

C:

\(8^{\text- 1}\)

D:

\(16^{\frac12}\)

E:

\(16^{\text- \frac{1}{2}}\)

F:

\(16^0\)

1:

\(\frac18\)

2:

\(\frac14\)

3:

\(\frac12\)

4:

1

5:

2

6:

4

Solution

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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   \(\frac13\)

Solution

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(From Unit 3, Lesson 3.)

Problem 5

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

Solution

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(From Unit 2, Lesson 11.)

Problem 6

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

Solution

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(From Unit 3, Lesson 4.)