algebra, law of exponents

1. Laws of Exponent
Product Rule
Quotient Rule
Product/Quotient to a Power
Power to a Power

2. LAWS OF EXPONENT
Express in exponential form or vise versa:
1. 2(2)(2) =
2. x(x)(x) =
3. (2x)(2x)(2x) =
4. (2x) 3 =
5. (xy)3 =
6. (𝑥
2
)3 =

3. Product Rule
copy the base ADD the exponent
Example:
1. (b2 ) (b3) =
2. (2x3) (3x5) =
3. (a2b) (a5b2) =

4. Quotient Rule
copy the base SUBTRACT the exponent
Example:
1. (
25
23 ) =
2. (
𝑥9
𝑥4 ) =
3. (
12𝑥5
2𝑥3 ) =

5. Product/Quotient to a Power
& Power to a Power Rule
Distribute the exponent by multiplying
Example:
1. (
𝑥2
𝑥
)5 =
2. (2x5y2)3 =
3. (
4𝑥5
2𝑥3 )2 =

6. Multiplication of polynomials
*apply the product rule*
-Multiply the constants
-Same variables will copy the base and Add the exponents

7. Find the product of the following polynomials
1. (3xy2 ) (4x3z) =
2. (3a) (4a2 + 3a – 5) =
3. (m – 4) (m + 3) =

8. (m – 4) (m + 3) =

9. Division of polynomials
*apply the Quotient rule*
-Divide the constants
-Same variables will copy the base and Subtract the exponents

10. Quotient Rule
copy the base SUBTRACT the exponent
1. (
25𝑥5𝑦2𝑧3
5𝑥𝑦3𝑧2 ) =
2. (
4𝑥8+6𝑥6−2𝑥4𝑦2−10𝑥2
2𝑥2 ) =

11. Assignment:
Special Products apply FOIL method
Example:
1. (x + 3) (x – 4)
2. (x – 5) (x – 5) =
3. (2x – 2)(2x + 2) =

12. Assignment:
Special Products apply FOIL method
Example:
1. (x + 3) (x – 4) =

13. Assignment:
Special Products apply FOIL method
Example:
2. (x – 5) (x – 5) =

14. Assignment:
Special Products apply FOIL method
Example:
3. (2x – 2)(2x + 2) =

15. Assignment:
Special Products apply FOIL method
1. (x + 9)(x + 4) =
2. (a – 5)(a – 5) =
3. (7x – 4y) (7x + 4y) =