1. EXPONENTS

2. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power.
Exponent
Base 7 2

3. Power- A number produced by raising a base to an exponent.
Exponential form-a number written with a base and an exponent
Exponent-shows how many times the base number is going to be multiplied
Base- the number that is used as a factor
Power- A number produced by raising a base to an exponent.

4. Writing as an EXPONENT Write in exponential form...
Identify how many times 4 is a factor.
4 • 4 • 4 • 4 = 44
B. (–6) • (–6) • (–6)
Identify how many times –6 is a factor.
(–6) • (–6) • (–6) = (–6)3
Read –(63) as “-6 to the 3rd power or -6 cubed”.
Reading Math

5. Find the product of five 3’s. 35 = 3 • 3 • 3 • 3 • 3
Evaluate.
A. 35
Find the product of five 3’s.
35 = 3 • 3 • 3 • 3 • 3
= 243
B. (–3)5
Find the product of five –3’s.
= (–3) • (–3) • (–3) • (–3) • (–3)
(–3)5
= –243
Helpful Hint
Always use parentheses to raise a negative number to a power.

6. Multiply Divide
Exponent of Negative Exponent Exponent

7. Multiply
Add the exponents
Keep the same base
32 x 33 = 32+3 = 35

8. Multiply: Write the product as one power
x5 • y2
Cannot combine; the bases are not the same.
x5 • y2
Add exponents.
412 • 417 41
2 + 7 41 9

9. Divide
Subtract the exponents
Keep the same base
36 = 36-2 = 34 32

10. 7 7 Subtract exponents. 7 x x Subtract exponents. x Think: x = x
Divide. Write the quotient as one power. 7 5 3 A. 7
5 – 3
Subtract exponents. 7 2 x 10 9 B. x
10 – 9
Subtract exponents. x
Think: x = x 1

11. (32)3 = 32x3 = 36 Exponent to Exponent Keep the same base
Multiply the exponents
(32)3 = 32x3 = 36

12. C. A. (54)2 (54)2 = 54 • 2 Multiply exponents. = 58 Simplify.
2 3 12 –3 C.
A. (54)2
(54)2
= 54 • 2
Multiply exponents.
2 3
12 • –3 =
= 58
2 3
–36 =

13. Negative Exponent
Put one over that number with a positive exponent
3-2 = 1 = 1

14. Negative Exponents
A negative exponent means divide, because the opposite of multiplying is dividing
Whenever you have an exponent that is negative, make it its reciprocal (Flip it!) and remove the sign.
4-3 = 4-3 = 1 1 62 = = 62 = 36
6-2 1 1 43

15. Zero Exponent
If a base other than zero is raised to a zero power it ALWAYS equals one.
50= 1
7380 =1
If zero is raised to a zero power it ALWAYS equals zero.

16. Exponent of 1
Anything raised to a power of 1 is itself because that shows that there is 1 of the base.
51= 5
X1= x

17. Power of a Product Find the power of each factor and multiply.
(6x)3= 63x3= 216x3
(xy)4= x4y4
(x/y)3= x3/y3

18. Evaluate: 5 – (6 – 4) -3 + (-2) 0
Do it on your own!

19. Review
When you…

20. Multiply- add exponents

21. Divide- subtract exponents
36 = 36-2 = 34 32

22. Exponent to Exponent- multiply

23. Negative Exponents- Flip over the bar and place a one if necessary
3-2 = 1 =

24. Exponents Multiply- Add exponents Divide - Subtract exponents
Exponent to Exponent- Multiply
Negative Exponents- Make the reciprocal