MULTIPYING POWERS

LESSON 15LESSON 15

4422

BASEBASE

EXPONENTEXPONENT

POWERPOWER

EXPONENT LAW 1EXPONENT LAW 1• PRODUCT OF POWERSPRODUCT OF POWERS

•nnaa x n x nbb = n = na+ba+b

•Multiplying Multiplying powers with powers with the same basethe same base

nnaa x n x nbb = n = na+b a+b (Product of (Product of Powers)Powers)• To multiply powers with

the same base:same base:

• KEEP THE BASEKEEP THE BASE• ADD THE EXPONENTSADD THE EXPONENTS

• EXAMPLE:EXAMPLE:•3333 x 3 x 344 = 3 = 377

WHY:• 33 = (3x3x3)• 34 = (3x3x3x3)

• Therefore:• 3333 x 3 x 344 = (3x3x3)

(3x3x3x3) = 3377

Meaning of the powerMeaning of the power

EXAMPLE•4444 x 4 x 499

• Write as a single Power• Write the meaning• Give the value

EXAMPLE:•4444 x 4 x 499 • Write as a Write as a single Powersingle Power•4444 x 4 x 499 = 4 = 41313

• Write the Write the meaningmeaning• (4x4x4x4)(4x4x4x4x4x4x4x4x4)• =(4x4x4x4x4x4x4x4x4x4x4x4x

4)• Give the Give the valuevalue• 413 = 67108864

EXAMPE 2: 5

== -4 5( )x

-4 5( )2 -4

5( )3

(1.1)(1.1)33 (1.1) (1.1)22(1.1) = (1.1)(1.1) = (1.1)66

Exponent of 1 Exponent of 1 you don’t have you don’t have to show itto show it

EXAMPLE 3 (4(433 x 4 x 455))33

= (43 x 45)(43 x 45)(43 x 45)

= (48)(48)(48)

= (48+8+8)=(424)SINGLE POWERSINGLE POWER

MEANINGMEANING

EXPONENT LAW 2• POWER OF A POWER

•(x(xmm))nn = x = xmnmn

• Multiply the two powers Multiply the two powers together.together.

• Example:Example:

• (5(522))33 = 5 = 566

EXAMPLE – (x(xmm))nn = x = xmnmn

(3(322 x 3 x 344))33

= (3= (366))33

= (3= (366)(3)(366)(3)(366))

= (3= (31818))

EXAMPLE 2 – Find the value NOT THE SAME BASENOT THE SAME BASE

FIND VALUE FOR FIND VALUE FOR EACH POWEREACH POWER

FOLLOW FOLLOW ORDER OF ORDER OF OPERATIONSOPERATIONS

(4(433 x 5 x 522))33

=(64 x 25)=(64 x 25)33

=(1600)=(1600)33

= 4 096 000 000= 4 096 000 000