MTH 091

Section 10.1Exponents

Introduction

• In this section we introduce some of the rules for dealing with exponential expressions.

• Other rules will be introduced in later sections.

• Recall that, when we evaluate an expression, we substitute and simplify according to the order of operations.

Examples

• Evaluate each of the following for x = -2, y = 1, z = 3:

5

2

44

32

3

z

yx

x

The Rules

10

a

aa

a

c

a

c

a

baab

aa

aaa

nmn

m

n

nn

nnn

mnnm

nmnmPRODUCT RULE: If you multiply with like bases, keep the base and add the exponents.

POWER RULE: If you raise a power to a power, keep the base and multiply the exponents.

POWER OF A PRODUCT AND QUOTIENT RULES: Exponents distribute over both products and quotients.

QUOTIENT RULE: If you divide with like bases, keep the base and subtract the exponents.

ZERO EXPONENT: Anything to the zero power is 1.

More Examples

4

115

131522

4

9152

2

53

ab

t

zyzy

yy

xxx

Still More Examples

02

0

3

9

4

332

77

5

5

3

ab

x

x

b

b

axy

Just A Couple More…

75

1312

3

4

5

6

3

yx

yx

x

y