Exponent Rules

0 1

m n m n

mm n

n

nm mn

a a a

aa

a

a

a a

1

a negative exponent

"means" take the

reciprocal of the base

mm

aa

Exponent Rules

3 2x

3 2x x

5x

Exponent Rules

7 2 42 3 x x y y

7 2 42 3x y xy

8 66x y

Simplify each algebraic expression.

Do NOT leave negative exponents.

4

9

14

7

m

m

2 7

1 7

mmmm

mmmmmmmmm

5

2

m

Exponent Rules

20 1281x y

45 33x y 5 3 5 3 5 3 5 33 3 3 3x y x y x y x y

Simplify the given expression. Do not leave negative exponents.

25

2

1

51

25

Simplify the given expression. Do not leave negative exponents.

Clear outside exponents first,

move the “location” of the base that has a negative exponent

the base still has an exponent, but now it is positive.

Simplify the given expression. Do not leave negative exponents.

22 1

5 2

y y

y y

25 2

2 1

y y

y y

10 4

4 2

y y

y y14

122

y

yy

Simplify the given expression. Do not leave negative exponents.

Clear outside exponents first, make sure all parenthesis are “gone” before “moving” bases.

The base is only what the exponent touches.

Simplify the given expression. Do not leave negative exponents.

2

4 3

x y

x y 2 3

4

x yy

x 2 4

4

x y

x 4

2

y

x

Simplify each numerical expression.

1mm

aa

1

mma an

m nma a

Negative exponent, take the reciprocal of the base

Rational exponent, rewrite as radical, the denominator is the index

Rational exponent, rewrite as radical, the denominator is the index, the numerator is still the exponent of the base.

Simplify each numerical expression.

1

2

25

2

1

1

25

1

25 1

5

Simplify each algebraic expression.

Do NOT leave negative exponents.

When working with rational exponents, the denominator of the exponent is the index of the radical, and the numerator is still the exponent of the base.

The base is only what the exponent “touches”.

Simplify each algebraic expression.

Do NOT leave negative exponents.

3 2

4 3

1

6

12

a a

a

9 8

2

a a

a3

1

a

Simplify each algebraic expression.

Do NOT leave negative exponents.

If n is a positive integer and m is any integer and is a real number, then

In radical notation:

m 1

m1/ n mn na a a

m

m n mnna a a

Simplify each algebraic expression.

Do NOT leave negative exponents.

1 14 6 6 122 3

6 2 9

x y x y

x y z

2 3 2 4

3 1 3

x y x y

x y z

0 7

3 1 3

x y

x y z

3

8 3

x

y z