Exponent Rules

2-6-3

Repeated Multiplication

Remember:

so

and

43 3(3)(3)(3) 4 3 73 3 3(3)(3)(3)(3)(3)(3) 3

5 3 8x x xxxxxxxx x

3 2 2 5 72 3 8 9 72 72s s ss sssss sssssss s

Multiplying with Exponents

Rule: so

and

When multiplying like bases, add the exponents.

m n m na a a 52 123 175f f f71 3

8 842 3 6w w w

3 5 5 3 5 1 5 8 63 4 12 12y z y z y z y z

Cancel Common Factors Remember how to cancel.

Make a 1 out of common factors.

14 6 7 2 7

4 15 2 5 5

52

3 1

r rrrrr rrrrr rrr

r rrr rrr

3

6 3

1 1h hhh

h hhhhhh hhh h

3 2

2 4 2

a b aaabb aaabb a a

a b aabbbb aabbbb bb b

Dividing with Exponents

Rule:

When dividing like bases, subtract the exponents.

Review the examples.

is the same as r 5-3

mm n

n

aa

a

543543 215 328

215

kk k

k

259

16

12 3

20 5

ss

s

52

3 1

r rrrrr rrrrr rrr

r rrr rrr

Negative Exponents Notice what happens with the example

33 6 3

6 3

1 1h hhhh h

h hhhhhh hhh h

1 1 and n n

n na a

a a

This leads to another rule.

Rule:

1 1 and n n

n na a

a a

When the Power is Zero

Rule: 0 1a Anything to the zero power is 1.

33 3 0

3

xx x

x or all cancel for an answer of 1.

Multiplying Exponents

nm mna aRule:

53 3 3 3 3 3 3 5 15x x x x x x x x

using a previous rule.

An easier way would be to multiply the 3 and 5 to get the new exponent of 15.

Unlike Terms are not like terms and cannot be combined. 3 25 3x x

Contrast this with 3 4 75 3 15x x x The multiplication can be done.

3 3 34 5 9m m m Don’t add the exponents.

3 3 64 5 20m m m Do add the exponents