1. MATH IS FUN!!!

2. Let’s start by reviewing exponent laws!

3. Multiplying powers …
If you are multiplying powers with the same base …
34 x 36
(here both numbers have a base of 3)
Then … you keep the base the same and ADD the exponents
34 x 36 = 3 (4 + 6)
= 310

4. Try These… (Do them on a sheet with your name and the date – they will be collected next class!)
Simplify.
(32)(34)
(43)(47)(42)
(53)(5)

5. Then … you keep the base the same and you SUBTRACT the exponents
Dividing powers …
If you are dividing powers with the same base … 75 73
Then … you keep the base the same and you SUBTRACT the exponents
75 ٪ 73 = 7 (5 - 3)
= 72

6. Do these on your page …
Simplify. 25 22
108
3. k4 k

7. Exponents of exponents …
If you have to simplify a power of a power with the same base …
(25)3
Then … keep the base the same and MULTIPLY the exponents
(25)3 = 25x3
= 215

8. Do these on your page … Express as a single power. (103)2 (2813)0
(6-1)-1

9. Sometimes exponents of exponents can get tricky!!
What happens when there are variables in the question?

10. (x2y3)(x4y2) This expression can also be written as
x2 x y3 x x4 x y2 = (x2 x x4) x (y3 x y2)
And we know that when we multiply powers with the same base, we ADD the exponents, so …
(x2 x x4) x (y3 x y2) = (x 2 + 4)(y 3 + 2)
= x6y5

11. Do these on your page …
Simplify.
(w-6)(w-7)
(x4)2
h-8
h-9

12. This is just like the last example!
(x2y3)3
In this case, the 3 outside the bracket must apply to EVERYTHING inside the bracket!
(x2y3)3 = (x2y3)(x2y3)(x2y3)
This is just like the last example! OR
We know that when we want to simplify the power of a power, we MULTIPLY the exponents
(x2y3)3 = (x2x3)(y3x3)
= x6y9

13. Do these on your page …
Simplify.
(x5y2)3
2. (mp)4(m5p)
3. (t3w9)(t2)5

14. But what if there are numbers and variables???
(-x2)100
The exponent must still be applied to EVERYTHING inside the bracket!
(-x2)100 is the same as (-1x2)100
In this case, the 100 applies to the -1 AND the x2
(-1x2)100 = (-1)100(x2)100
= 1x 2x100
= 1x200

15. Do these on your page … Simplify. (-10y5)4 (3m2)2
(5h5m3)  remember the 9 applies to everything in the brackets … (the 5, the h5 and the m3)

16. Ok, now for something a little bit new!!!
You know how to simplify expressions with exponents, but sometimes you are asked to evaluate them after they are simplified.
BUT … what do you do with a negative exponent?!?

17. (3-2)(3-1)
We know that when we multiply powers with the same base, we ADD the exponents …
(3-2)(3-1) = 3( )
= 3-3
How do we evaluate this??

18. 3-3
Anytime you have a negative exponent, you can make it into a positive exponent by putting a 1 over number!
3-3 = 1 33
= 1 9

19. Let’s see another one of those …
If we have the following:
5-7  remember we SUBTRACT the
exponents
5-7 = 5( ) = 5-4
5-3
Now, we simply put 5-4 under a 1  1_
54 (it becomes positive)
And we can evaluate it as we would any positive exponent …
1 = 1

20. Jorge – try it on your own first!!!
Do these on your page …
From page 230 in your textbook:
Questions 9, 10 and 11(a, c, e)
Remember I will be collecting this work next class! If you have difficulty, review the slides and then ask one of your classmates to help you!
Jorge – try it on your own first!!!

21. HAVE A GREAT DAY!!!