1. Powers of Monomials
Chapter 4
Section 4.4

2. Objective
Students will find powers of monomials

3. Concept
To find a power of a monomial that is already a power, you can use the definition of a power and the rule of exponents for products of powers.

4. Concept
Example: (x5)3 x5 * x5 * x5 x5+5+5 x15

5. Rule of Exponents for a Power of a Power
For all positive integers m and n: (am)n = amn To find a power of a power, you multiply the exponents.

6. Example
(x4)5

7. Example
(m5)3

8. Example
[(-a)2]3

9. Concept
To find a power of a product, you can use the definition of a power and the commutative and associative properties of multiplication.

10. Concept
Example: (2x)3 (2x)(2x)(2x) (2 * 2 * 2)(x * x * x) 23 * x3 8x3

11. Rule of Exponents for a Power of a Product
For every positive integer m: (ab)m = ambm To find a power of a product, you find the power of each factor and then multiply

12. Example
(-2k)5

13. Example
Evaluate if t = 2 3t3 (3t)3 33t3

14. Questions

15. Assignment
Worksheet