Math 7 (Period 4)

Multiplying and Dividing Powers 6.7

 We are discovering the basic multiplication rules for powers having the same bases.

Multiplying Powers

a⁵ ∙a³= a∙a∙a∙a∙a∙a∙a∙a = a⁸

 RULE….to multiply two powers with the SAME BASES just add their exponents

a^m ∙ aⁿ = a^m+n

3²∙3³ = 3⁵

( -½)² (-½ )  = (-½ )³

Multiplygin Variable Expressions:

2x²∙3x⁴ = (2∙3)(x²∙x⁴) = 6x²⁺⁴ = 6x⁶

Dividing Powers

c⁵/c³

c∙c∙c∙c∙c
c∙c∙c

= c∙c

= c²

c⁵/c³ = c^5-3 = c²

To divide two powers with the SAME BASES just subtract the exponents

a^m/aⁿ = a^m-n

2⁷/2⁴= 2^7-4 = 2³

(-5)³/-5

Careful with this one… it is really

(-5)³/(-5)¹

Now they are the same base so it is just a subtraction problem with the exponents

(-5)^3-1 =(-5)² = (-5)(-5) = 25

So let’s look at two examples

(-2)⁵ means (-2)(-2)(-2)(-2)(-2) = -32

But

(-2)⁴ means  (-2)(-2)(-2)(-2) = + 16

(-2)¹¹ à negative

(-2)¹⁰ à positive

***Odd/Even Rule with powers***

If there is a negative inside the parentheses

odd # of negative signs or odd  power à it will be negative

even # of negative signs or even power à it will be positive

(-4) ⁵⁵ à negative

(-4)⁵⁶ à positive

(-1)¹⁵ = -1

(-1)¹⁰⁰ = +1

If there is a negative but NO parentheses (NO HUGS!!)

such as -2⁵ or -2⁴

….IT will ALWAYS be negative

-2⁵ means take the opposite of 2⁵

and -2⁴ means take the opposite of 2⁴

-2⁵ = -2∙2∙2∙2∙2 = -32

-2⁴ =   -2∙2∙2∙2 = -16

(-10)⁴/(-10)² = (-10)^4-2 = (-10)²

Be careful

-10² ≠ (-10)²

-100 ≠ 100

(2/5)⁶
(2/5)³

= (2/5)^6-3

=8/125