Algebra Honors (Period 6 & 7)

Powers of Monomials 4-4


POWER TO ANOTHER POWER


MULTIPLY the POWERS
(m⁵)³ = m¹⁵


To check, EXPAND it out:
(m⁵)(m⁵)(m⁵) = m¹⁵



PRODUCT TO A POWER

DISTRIBUTE the power to EACH FACTOR
(m⁵n⁴)³ = m¹⁵n¹²



(a^m)ⁿ = a ^mn
(u⁴)⁵ = u²⁰
(2x)³ = (2x)(2x)(2x) = 8x³

(ab)^m = (ab)(ab)(ab).... -->m factors<--- = (a⋅a⋅a⋅a⋅a ...)(b⋅b⋅b⋅b⋅b ...) where a is multiplied m number of times and b is multiplied m number of times.... (ab)^m = a^mb^m
To find the power of a product, you find the power of each factor and then multiply

Simplify
(-2k)⁵
= (-2)⁵ k⁵ = -32k⁵

Evaluate if t = 2
a) 3t³
b) (3t)³
c) 3³t³
d) -(3t)³


Simplify
(-3x²y⁵)³
(-3)³(x²)³(y⁵)³
-27x⁶y¹⁵



RAISING A QUOTIENT TO A POWER:


DISTRIBUTE THE POWER to the numerator and the denominator

(m²/n⁶)³ = m⁶/n¹⁸

1/n⁶ = n^-6
so what does
1/m^-7 =?

Let's read it in math terms
it is 1 divided by 1/m⁷ .. and what do you do when you need to divide by a fraction? You multiply by its reciprocal so

1 divided by 1/m⁷ = 1 ÷ 1/m⁷ = 1× m⁷/1 = m⁷