Powers of Monomials Chapter 4 Section 4.4

Objective Students will find powers of monomials

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.

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

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.

Example (x4)5

Example (m5)3

Example [(-a)2]3

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

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

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

Example (-2k)5

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

Questions

Assignment Worksheet