1. PROPERTIES of EXPONENTS

2. 3 Location of Exponent 4 Exponent Base
An exponent is a little number high and to the right of a regular or base number. 3 4
Exponent
Base

3. Definition of Exponent
An exponent tells how many times a number is multiplied by itself. 3 4
Exponent
Base

4. What an Exponent Represents
An exponent tells how many times a number is multiplied by itself. 4
= 3 x 3 x 3 x 3 3

5. How to read an Exponent
This exponent is read three to the fourth power. 3 4
Exponent
Base

6. Properties

7. MULTIPLYING POWERS WITH THE SAME BASE
Words
Numbers
Algebra
To multiply powers with the same base, keep the base and add the exponents.
bm • bn =
bm + n
35 • 38 =
= 313
MULTIPLYING POWERS WITH THE SAME BASE

8. Together! Alone! 1. 66 • 63 1. 42 • 44 2. x2 • x3 2. n5 • n7
3. x5 • y2
3. 25 • 2
• 417
• 244

9. Multiplying Power of a Power
Words
Numbers
Algebra
To multiply power of a power, keep the base and multiply the exponents.
Multiplying Power of a Power
(pr)s =
pr • s
NOTE:
Multiply the exponents, not add them!

10. 1. (y4)2 1. (x2)3 2. (55)2 3. (3²)⁴ 4. (4)² 2. (3)6 3. (2⁶)² 4. (6²)³
Together!
Alone!
1. (y4)2
1. (x2)3
2. (55)2
3. (3²)⁴
4. (4)²
2. (3)6
3. (2⁶)²
4. (6²)³

11. Power of a Product (a · b)ᴹ = aᴹ · bᴹ Example (5 · 7)² = 5² · 7²
To raise a product to a power, raise each factor to the power
Example (5 · 7)² = 5² · 7²
(4x)³ = 4³ · x³

12. 1. (3y)2 1. (7x)3 2. (5 · 3)2 3. (3²x³)⁴ 4. 3² · 5² 2. (3 · 2)6
Together!
Alone!
1. (3y)2
1. (7x)3
2. (5 · 3)2
3. (3²x³)⁴
4. 3² · 5²
2. (3 · 2)6
3. (2⁶x)²
4. 4³ · 2³

13. 1.) b2 • b7 2.) (p3)4 3.) (a2)3 • a3 4.) x2 • (xy)2 5.) (4m)2 • m3
6.) (3a)3 •(2p)2
7.) w3 • (3w)4
8.) 7² · 3²
9.) (3² x³)⁴
10.)(x2y3)2
Pair- Practice!

14. Ex:
Multiplying Polynomials:
In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base.

15. Please simplify the following equations:
How?:
Answer:

16. Division Properties of Exponents

18. Finding Quotients of Powers
Simplify
Alone
Together A. A. B. B. C. C. D. D.

20. Finding Positive Powers of Quotient
Simplify.
Alone
Together A. A. B. B. C. C.

21. Remember that What if x is a fraction?

22. Finding Negative Powers of Quotients
Simplify.
Alone
Together A. A. B. B. C. C.