Lesson 3

Exponents That Are Unit Fractions

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Problem 1

Complete the table. Use powers of 64 in the top row and radicals or rational numbers in the bottom row.

\(64^1\) \(64^{\frac12}\)   \(64^0\)   \(64^{\text-1}\)
64   4   \(\frac18\)  

Solution

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Problem 2

Suppose that a friend missed class and never learned what \(25^{\frac12}\) means.

  1. Use exponent rules your friend would already know to calculate \(25^{\frac12} \boldcdot 25^{\frac12}\).
  2. Explain why this means that \(25^{\frac12}=5\).

Solution

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Problem 3

Which expression is equivalent to \(16^{\frac12}\)?

A:

\(\frac14\)

B:

4

C:

8

D:

16.5

Solution

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Problem 4

Select all the expressions equivalent to \(4^{10}\).

A:

\(2^5 \boldcdot 2^2\)

B:

\(2^{20}\)

C:

\(4^4 \boldcdot 4^6\)

D:

\(4^7 \boldcdot 4^{\text- 3}\)

E:

\(\frac{4^4}{4^{\text-6}}\)

Solution

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(From Unit 3, Lesson 1.)

Problem 5

The table shows the edge length and volume of several different cubes. Complete the table using exact values.

edge length (ft) 3             \(\sqrt[3]{100}\)   \(\sqrt[3]{147}\)
volume (ft3)       64 85   125  

Solution

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(From Unit 3, Lesson 2.)

Problem 6

A square has side length \(\sqrt{82}\) cm. What is the area of the square?

A:

9.05 cm2

B:

82 cm2

C:

164 cm2

D:

6724 cm2

Solution

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(From Unit 3, Lesson 2.)