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
\(\sqrt{23}\)