Lesson 2 Twin Powers Solidify Understanding

Ready

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

Example: Rewrite .

Example: Rewrite .

1.

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.

14.

15.

16.

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 .