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9-12 Algebra 2 Unit 4 Lesson 5

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Unit 4, Lesson 5

Negative Rational Exponents

Algebra 2

Practice

Problem 1

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

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

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Problem 2

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

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Problem 3

Match the equivalent expressions.

\(8^{\frac13}\)
\(8^{\text- \frac13}\)
\(8^{\text- 1}\)
\(16^{\frac12}\)
\(16^{\text- \frac{1}{2}}\)
\(16^0\)

\(\frac18\)
\(\frac14\)
\(\frac12\)
1
2
4

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Problem 4

ForLesson 3: Exponents That Are Unit Fractions

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		\(\frac13\)

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Problem 5

ForLesson 11: Finding Intersections

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

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Problem 6

ForLesson 4: Positive Rational Exponents

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

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Lesson 5 Resources

Student Materials