Simplifying Exponents

How do I know when it is simplified???

Only one of each base

Constants simplified

NO negative or zero exponents

3xIt tells you It tells you how many how many times to times to

multiply a multiply a base by base by itself.itself.

5x xxxxx =

43 xx )()( xxxxxxx

7x

=

=

Action Rule Example

Multiply Two Powers

ADD the exponents

x5x7= x12

Exponent Rules

))(4( 3442 cabbca

23)(x

23)(x33 xx

6x

)()( xxxxxx

=

=

=

Exponent Rules

Action Rule Example

Multiply Two Powers

ADD the exponents

x5x7= x12

Power to a power

MULTIPLY the exponents

(x3yz4)5 = x15y5z20

242 )3( yzx

5x 9yz4

3

Exponent Rules

Action Rule Example

Multiply Two Powers

ADD the exponents

x5x7= x12

Raise power to a power

MULTIPLY the exponents

(x3yz4)5 = x15y5z20

Divide Two Powers

SUBTRACT the exponents

4x 5y 2

8x 3y 7x 2

2y 5

EXAMPLE #1EXAMPLE #1

2

4

x

x

6

2

y

y

4a2c8a2c 5

Action Rule Example

Zero Power =1 x0= 1x3y0=x3

10x

0000,000,1 1

QUESTION:QUESTION:What happens What happens when a zero when a zero exponent is exponent is

embedded in embedded in an exponent an exponent expression?expression?

020 cba

EXAMPLE

NEGATIVE EXPONENTS

OK. TOO EASY OK. TOO EASY FOR YOU.FOR YOU.

BUT CAN YOU BUT CAN YOU HANDLE HANDLE

NEGATIVE NEGATIVE EXPONENTS?EXPONENTS?

Action Rule Example

Zero Power =1 x0= 1x3y0=x3

Negative Exponents

Flip it

x 2 1

x 2

1

y 5 y 5

x 5

1

x 9

x 5y 0x 4EXAMPLE

7x 3y 5

az 4

EXAMPLE

(2x 5y 73x 4y)3EXAMPLE

4x 4y 8z 11

8a3x 3y14

EXAMPLE

3x 3y 7z5

4 1y 4z 8

EXAMPLE

6x 4y 3z

y 5

EXAMPLE

4a3b6 3 3a 5b4 2EXAMPLE