# Lesson 3

Exponents That Are Unit Fractions

### 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.

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

### Solution

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### Problem 3

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

\(\frac14\)

4

8

16.5

### Solution

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### Problem 4

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

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

\(2^{20}\)

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

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

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

### 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 (ft^{3}) |
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?

9.05 cm^{2}

82 cm^{2}

164 cm^{2}

6724 cm^{2}

### Solution

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(From Unit 3, Lesson 2.)