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.

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) volume (ft3) 3 $$\sqrt[3]{100}$$ $$\sqrt[3]{147}$$ 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.)