Lesson 3
Exponents That Are Unit Fractions
- Let’s explore exponents like \(\frac12\) and \(\frac13\).
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 | \(\frac18\) |
Problem 2
Suppose that a friend missed class and never learned what \(25^{\frac12}\) means.
- Use exponent rules your friend would already know to calculate \(25^{\frac12} \boldcdot 25^{\frac12}\).
- Explain why this means that \(25^{\frac12}=5\).
Problem 3
Which expression is equivalent to \(16^{\frac12}\)?
A:
\(\frac14\)
B:
4
C:
8
D:
16.5
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:
(From Unit 3, Lesson 1.)
\(\frac{4^4}{4^{\text-6}}\)
Problem 5
The table shows the edge length and volume of several different cubes. Complete the table using exact values.
edge length (ft) | 3 | \(\sqrt[3]{100}\) | \(\sqrt[3]{147}\) | |||
---|---|---|---|---|---|---|
volume (ft3) | 64 | 85 | 125 |
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:
(From Unit 3, Lesson 2.)
6724 cm2