Pre Algebra (Period 2 & 4)

Powers of Products & Quotients 5-9

(4∙2)³ = (4∙2)∙(4∙2)∙(4∙2)
= 4∙4∙4∙2∙2∙2
= (4∙4∙4)∙(2∙2∙2)
=4³∙2³

Raising a Product to a Power

(5∙3) ⁴ = 5³∙3³

or Algebraically:
(ab)^m = a^mb^m

Remember to simplify an expression, you write it with NO like terms or paranthese.

Simplify (4x²)³
Raise each factor to the power 3
= 4³∙x²∙³
Use the rule for Raising a Power to a Power
=4³∙x⁶
simplify
= 64x⁶

WE did several of these in class:
(2p)⁴ = (2∙2∙2∙2)∙(p∙p∙p∙p)
= 16p⁴

(xy²)⁵ = x⁵y¹⁰

(5x³)² = 25x⁶

The location of a negative sign affects the value of an expression. Look at the differences between the following

(-5x² = (-5)²x² = (-5)(-5)x² = 25x²

-(5x)² = - (5)(5)x² = -25x²


(-2y)⁴ = 16y⁴
-(2y)⁴ = -16y⁴

Do you see the subtle differences? Make sure you can determine why one is postive and the other is negative

Finding Powers of Quotients

(4/5)³ = (4/5)(4/5)(4/5)

or
4∙4∙4
5∙5∙5
=
4³
5³
= 64/125

To raise a quotient to a power, raise both the numerator and the denominator to the power

(2/3)⁴ =

2⁴
3⁴
=
16/81

(1/2)³ =
1/8

(-2/3)⁴
16/81

Why is it positive?

(2x²/3)³=

8x⁶/27


∙∙∙