1. Exponents Warm UP!
For each of the following problems, identify the base and the exponent:
1. 47
***If a number doesn’t have an exponent, then you can always assume that the exponent is one. For example, 7 = 71

2. Monomials vs. Polynomials

3. Monomial A monomial may be… A constant A variable
A product of a constant and variable

4. Polynomial Polynomial- Examples of Polynomials: 6x + 4 15h − 17k2
m3 + 2m2 − 4m + 11

5. What is an exponent?
An exponent is a superscript, or small number written at the top right corner of a number, variable, or set of parentheses

6. Example 23
Tells you to multiply the base by itself as many times as the exponent says.
2 * 2 * 2 8

7. -36
Note this negative sign in front of the 3. Because there are no parentheses, you leave the negative sign till the end
Write this out

8. (-3)6
Notice this problem has parentheses with a negative sign on the inside. This time you take the negative into account
Write it out

9. Negatives inside parentheses
If the exponent is even, the answer will be positive
If the exponent is odd, the answer will be negative.

10. Laws of Exponents

11. crcs=cr +s add exponents
(5t)(−30t2)
(−4a2b)(1ab3)
(2x2y)(xz3)(3y2z2)

12. What do I do with negative exponents?
Subtract!
(4x3)(x-2)
(3y4)(2y-1)

13. Tic Tac Toe!
Decide who will be the x in the group and who will be the o. Choose a problem to simplify. Both you and your partner should solve the problem. If you answered correctly, put your letter on top of the problem. Have your partner choose a problem to solve and repeat the steps above.

14. Powers raised to powers
(23)4 can be written out similar to the way we wrote out exponents in the beginning
Now you just need to write the power out the exponent attached to the number each time as well.

15. Examples

16. A faster trick You can multiply when you have a power to a power
Looks different from the addition case
(2x3)(3x4)
(2x3)2

17. (26)2

18. (104)2

19. (y3)5

20. (m3)x

21. Going one step farther
When there is a number or extra variable in the parentheses, you must distribute the power outside the parentheses to both things
(4x)2

22. Another
(xy)3

23. (gm)6

24. (4w)3

25. Exponents with Fractions
Square the term in the numerator
Square the term in the denominator
Simplify if possible

27. Division of exponents

28. One catch
You may only subtract exponents with the same bases

29. c4b
c2a
−4x2y5
2xy3