Lesson 5 Twin Powers Solidify Understanding

Ready

Rewrite each of the radical expressions to remove perfect square factors from inside the radical.

Example: Rewrite $\sqrt{20}$ .

$\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{2 \cdot 2 \cdot 5} = 2 \sqrt{5}$

Example: Rewrite $\sqrt[5]{96}$ .

$\sqrt[5]{96} = \sqrt[5]{2^{5} \cdot 3} = 2 \sqrt[5]{3}$

1.

$\sqrt{40}$

2.

$\sqrt{50}$

3.

$\sqrt[3]{16}$

4.

$\sqrt{72}$

5.

$\sqrt[4]{81}$

6.

$\sqrt{32}$

7.

$\sqrt[5]{160}$

8.

$\sqrt{45}$

9.

$\sqrt[3]{54}$

Set

10.

Finish filling in the table of values for $y = 3^{x}$ and use it to explain the meaning of $3^{- 2}$ .

$x$	$- 4$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$y$					$1$	$3$	$9$

Explanation:

11.

If two expressions with exponents are a perfect match except one has a negative exponent and the other has a positive exponent, like $5^{3}$ and $5^{- 3}$ , how does the exponent change the meaning of the expression?

For problems 12 and 13, use the graph of $y = 2^{x}$ and $y = {(\frac{1}{2})}^{x}$ .

12.

How does the graph show the relationship between $2^{3}$ and ${(\frac{1}{2})}^{- 3}$ ?

13.