# Lesson 4

Positive Rational Exponents

- Let’s use roots to write exponents that are fractions.

### Problem 1

Evaluate \(8^{\frac53}\).

### Problem 2

Select **all **expressions that are equal to \(64^{\frac32}\).

96

\(8^3\)

512

\(4^2\)

\(\sqrt{64^3}\)

\(\sqrt[3]{64}^2\)

### Problem 3

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

### Problem 4

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

### Problem 5

Select **all** items equivalent to \(\sqrt{24}\).

the area of a square with side length 24 units

the side length of a square with area 24 square units

the positive number \(x\), where \(x \boldcdot x = 24\)

the positive number \(y\), where \(y = 24 \boldcdot 24\)

the edge length of a cube with volume 24 cubic units

the volume of a cube with edge length 24 units

### Problem 6

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

\(\frac{1}{23} \)

\(\frac{1}{\sqrt{23}}\)

11.5

\(\sqrt{23}\)