Purpose: To find powers of monomials. This involves multiplying them as well. Homework: p odd.

Definitions When you take a monomial, x 5, and take it to a higher power, (x 5 ) 3 it is the same as this: –x 5  x 5  x 5 which is x 15 Rule: –(a m ) n = a mn To find the powers, you multiply the exponents or simply write it out as above.

Definitions (cont.) Power of a Product: –(ab) m = a m b m You need to find the power of each factor then multiply: –Example: (-4mn)³ = (-4)³m³n³ = -64m³n³

Chalkboard Examples 1. (m³) 4 = m³  m³  m³  m³ = m 12 OR 3  4 = 12 so m (x²) 5 = x [(-b) 4 ] 5 = (b 4 ) 5 = b (2y) 4 = 2y  2y  2y  2y = 16y 4 5. (4a 3 b 2 ) 4 = (4) 4 (a 3 ) 4 (b 2 ) 4 = 256a 12 b 8

Last Example #34 p. 157 (a²) 6, (-2a 4 ) 3 Simplify First. a 12, -8a 12 Now you are ready to add because they are like terms. a 12 + (-8a 12 ) = -7a 12 Now you can multiply the two monomials. (a 12 )(-8a 12 ) = -8a 24