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:

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

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.)