# Lesson 4

Positive Rational Exponents

### Problem 1

Evaluate $$8^{\frac53}$$.

### Solution

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### Problem 2

Select all expressions that are equal to $$64^{\frac32}$$.

A:

96

B:

$$8^3$$

C:

512

D:

$$4^2$$

E:

$$\sqrt{64^3}$$

F:

$$\sqrt{64}^2$$

### Solution

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### Problem 3

Write the expression $$17^{\frac43}$$ using radicals.

### Solution

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### Problem 4

An arithmetic sequence $$k$$ starts 4, 13, . . . . Explain how you would calculate the value of the 5,000th term.

### Solution

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(From Unit 1, Lesson 8.)

### Problem 5

Select all items equivalent to $$\sqrt{24}$$.

A:

the area of a square with side length 24 units

B:

the side length of a square with area 24 square units

C:

the positive number $$x$$, where $$x \boldcdot x = 24$$

D:

the positive number $$y$$, where $$y = 24 \boldcdot 24$$

E:

the edge length of a cube with volume 24 cubic units

F:

the volume of a cube with edge length 24 units

### Solution

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(From Unit 3, Lesson 2.)

### Problem 6

Which expression is equivalent to $$23^{\frac12}$$?

A:

$$\frac{1}{23}$$

B:

$$\frac{1}{\sqrt{23}}$$

C:

11.5

D:

$$\sqrt{23}$$

### Solution

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(From Unit 3, Lesson 3.)