mth 091 section 10.1 exponents. introduction in this section we introduce some of the rules for...
TRANSCRIPT
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