Lesson 5 Twin Powers Solidify Understanding

Ready

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

Example: Rewrite .

Example: Rewrite .

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2.

3.

4.

5.

6.

7.

8.

9.

Set

10.

Finish filling in the table of values for and use it to explain the meaning of .

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 and , how does the exponent change the meaning of the expression?

For problems 12 and 13, use the graph of and .

A graph of two functions on the same coordinate plane. One function is y=2 to the power of x. The other function is y= one half to the power of x. x–5–5–5555y555000

12.

How does the graph show the relationship between and ?

13.

What is true about the input values for each equation that produce the same output value?

Rewrite each of the expressions in an equivalent form with only one positive exponent.

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17.

Go

Find the indicated values for each of the problems.

18.

a.

Find .

b.

Find if .

c.

Find .

19.

a.

Find .

b.

Find if .

c.

Find .

20.

a.

Find .

b.

Find if .

c.

Find .

21.

a.

Find .

b.

Find if .

c.

Find .

22.

a.

Find .

b.

Find if .

c.

Find .

23.

a.

Find .

b.

Find if .

c.

Find .