§ 1.6 properties of integral exponents. blitzer, algebra for college students, 6e – slide #2...
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§ 1.6
Properties of Integral Exponents
Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.6
Properties of Exponents
Exponent Rules
Product Rule
Quotient Rule
nmnm bbb
0, bbb
b nmn
m
When multiplying exponential expressions with thesame base, add the exponents.
When dividing exponential expressions with the same nonzero base, subtract the exponentin the denominator from the exponent in the numerator.
Blitzer, Algebra for College Students, 6e – Slide #3 Section 1.6
Properties of Exponents
Exponent Rules Examples
Product Rule
Quotient Rule
10253253 qqqqq
133676342
7634274632
1212
3434
cbacba
ccbaacacba
22212
4623354
6
2
3
3
5
423
635
22
29
18
9
18
qtrtqr
tqrt
t
q
q
r
r
tqr
tqr
5383
8
zzz
z
Blitzer, Algebra for College Students, 6e – Slide #4 Section 1.6
Properties of Exponents
Your Turn!
€
(4x 3y 4 )(10x 2y 6)
Multiply using the product rule. Divide using the quotient rule.
€
27x14y 8
3x 3y 5
Blitzer, Algebra for College Students, 6e – Slide #5 Section 1.6
Properties of Exponents
The Zero Exponent Rule:
If b is any real number other than 0, then 10 b
Negative Exponent Rule: If b is any real number other than 0 and n is a natural number, then
nn
bb
1 n
nb
b
1and
Blitzer, Algebra for College Students, 6e – Slide #6 Section 1.6
Properties of Exponents
1170
11503423 zyx
2
2 1
xqxq
53
4
54
3543 1311
1313RP
Q
RQ
PRQP
Exponent Rules Examples
Zero Exponent Rule
Negative Exponent Rule
Blitzer, Algebra for College Students, 6e – Slide #7 Section 1.6
Properties of Exponents
3
26
2
63 44
x
pqy
pq
yx
115244433243243
2 3232
xx 4433
6
63232 1
dddd
Exponent Rules Examples
Negative Exponents in Numerators and Denominators
Power Rule
Blitzer, Algebra for College Students, 6e – Slide #8 Section 1.6
Properties of Exponents
Your Turn!Simplify using the Zero-exponent rule.
Simplify using the Negative-exponent rule.€
(−5x)0
€
3x −6y 4
Simplify using thePower to power rule.
€
(y 7)−2
Blitzer, Algebra for College Students, 6e – Slide #9 Section 1.6
Properties of Exponents
812424342434423 25625644 yxyxyxyx
18
12
1812
318123
3634336343364
8
51
2
1525
252525
b
a
baba
bababa
42
6
222
23
2222
232
22
232
2
3223
49
9
49
9
7
3
7
3
7
3
7
3
hf
g
hf
g
hf
g
fh
g
fh
g
f
hg
12
8
43
42
43
424
3
2
b
a
b
a
b
a
b
a
Exponent Rules
Examples
Products to Powers
Quotients to Powers
Blitzer, Algebra for College Students, 6e – Slide #10 Section 1.6
Properties of Exponents
Your Turn!
Simplify using the Product to Powers rule.
Simplify using the Quotient to Powers rule.
€
(−3x −1y 3)−2
€
x −4y 7
2
⎛
⎝ ⎜
⎞
⎠ ⎟
−5
Blitzer, Algebra for College Students, 6e – Slide #11 Section 1.6
Properties of Exponents
Of I M P O R T A N CE to note…
Be sure you pay special attention to the study tip on the bottom of page 72. This tip will help you avoid common errors
that can occur when simplifying exponential expressions.