1. Objective: Evaluate expressions with rational exponents.

2. Example 1:
Negatives in the exponents tell you to take the reciprocal (flip the fraction).
5 -3
=(1/5) 3
=1/125

3. Example 2:
The negative exponent tells me to flip the fraction.
(3/4) -2
=(4/3) 2
=16/9

4. Example 3:
A fraction in the exponent tells me to take the root. If the fraction has a two in the denominator, I take the square root. If it has a three in the denominator, I take the cube root. With a four, take the fourth root and so on.
16 1/2
= 4

5. Example 4:
The fraction in the exponent tells me to take the cube root, and the two in the numerator tells me to square what’s left after that.
8 2/3
=2 2
= 4

6. Example 5:
This exponent is telling me to take the square root, and to take the square root of a fraction, just take the square root of the top and the square root of the bottom.
(9/16) 1/2
= 3/4

7. 9 -3/2 =(1/9) 3/2 =(1/3) 3 =1/27 Example 6:
The negative exponent tells me to flip the fraction.
9 -3/2
=(1/9) 3/2
The two tells me to take the square root.
=(1/3) 3
The three tells me to raise it to the third power.
=1/27

8. (81/16) -3/4 =(16/81) 3/4 = (2/3) 3 = 8/27 Example 7:
The negative exponent tells me to flip the fraction.
(81/16) -3/4
=(16/81) 3/4
The four tells me to take the fourth root.
= (2/3) 3
The three tells me to raise it to the third power.
= 8/27

9. (125/8) 0 = 1 Example 8: Anything to the zero power is…
For homework, do your worksheet.

10. Exponential Equations

11. These are called exponential equations because the variable is in the exponent.
Always try to get the bases the same so that you can set the exponents equal to each other.
Example 1:
Now solve.

12. Since these bases didn’t begin the same, how can we write them the same?
Remember, you can only replace something with something that it is equal to.
Example 2:
Now set the exponents equal to each other and solve.

13. Example 3: Get the bases alike.
Now set the exponents equal to each other. Don’t forget to distribute.
Example 3:

14. Example 4: Get the bases alike.
Now set the exponents equal to each other. Don’t forget to distribute.
Example 4:

15. Example 5: Get the bases alike. How do you get the fraction to “flip”?
Use negative exponents.
Example 5:

16. Example 6: Get the bases alike.
Now set the exponents equal to each other. Don’t forget to distribute.
Example 6:

17. Answers to worksheet:

18. Answers to warm up exercises:
1/9
1/125 16
27/8
25/16 3
7) 125
8) 4
9) 3/5
10) 1/64
11) 8/27
12) 1