Multiplying and Dividing Multiplying and Dividing Powers with Same BasePowers with Same Base

Alex DrennanAlex Drennan

DefinitionsDefinitions

A power is the value indicated by a base A power is the value indicated by a base with an exponent:with an exponent:

ExponentExponent

BaseBase

MultiplyingMultiplying

To multiply powers with the same To multiply powers with the same base, keep the base the same and add base, keep the base the same and add the exponentsthe exponents

aamm x a x ann = a = am+nm+n

Example 1Example 1

1.1. 334 4 x x 3355

2.2. 334 4 x 3x 355 = 3 = 34+54+5

3.3. 334 4 x 3x 355 =3 =399

1.1. Recognize same Recognize same basebase

2.2. Add the Add the exponentsexponents

3.3. SolveSolve

Example 2Example 2

1.1. 22-4-4 x x 2255

2.2. 22-4-4 x 2 x 255 = 2 = 2-4+5-4+5

3.3. 22-4-4 x 2 x 255 = 2 = 211

4.4. 2211 = 2 = 2

1.1. Recognize Recognize same basesame base

2.2. Add the Add the exponentsexponents

3.3. SolveSolve4.4. Any number to Any number to

the first power the first power equals itselfequals itself

DividingDividing

To divide powers with the same base, To divide powers with the same base, subtract the exponent in the subtract the exponent in the denominator from the exponent in the denominator from the exponent in the numeratornumerator

aamm aam-nm-n

aann =

Example 1Example 1

1.1. 4477

2.2. 4477

3.3. 4477

1.1. Recognize same Recognize same basebase

2.2. Subtract the Subtract the exponentsexponents

3.3. SolveSolve

4455

4455= 47-5

4455= 42

Example 2Example 2

1.1. 2233

2.2. 2233

3.3. 2233

4.4. 22-5-5 = = 11

1.1. Recognize same Recognize same basebase

2.2. Subtract the Subtract the exponentsexponents

3.3. SolveSolve

4.4. Negative Negative exponent moved exponent moved to denominatorto denominator

2288

2288 = 23-8

2288 = 2-5

2255