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Math 10 Name: Unit 2: Roots and Powers (Day 4)
Exponential Notation Cont.
A negative exponent in the denominator becomes a positive exponent in the numerator:
i) 42
1
ii) 26
1
iii) 33
1
iv) 27
1
ex: Rewrite with positive exponents:
i) 263
122
fed
bca ii)
31
2343
ts
rqp
Ex: Use a power with a negative exponent (other than -1) to write an equivalent form for:
i) 81
1 ii)
27
1 iii) 9
I. Rational Exponents
A radical can be changed into a fractional exponent or a fractional exponent can be changed into
as radical as follows:
b
aa
b xx
Examples: Evaluate
i) 3
2
27 ii) 2
5
4
iii) 2
3
16
9
iv) 3
5
)8(
v) 5.036 vi) 6.032
vii) 75.016 viii) 5.064.0
Write each number as a power with exponent 2
1
i) 5 ii) 7
Write in exponential form: nx
i) 5
7 12 ii)
8
2
5
iii)
5
3
2
iv)
3 95
Examples:
i) )7)(5( 243 xyyx ii) 92
45
6
9
yx
yx
iii) 362 )3( yzx
* The power law is always done before the multiplication and division laws *
iv) 322 )2)(5( baab v) 22
3422
)4(
)8)(6(
mn
nmnm
vi) 25
2242
)6(
)2()3(
dc
cddc
II. Combining Negative Exponents and Fractional Exponents
ab
b
ab
a
xx
x11
i) 4
3
16
ii) 3
2
27
iii) 2
3
16
9
iv) 6.032
v) 2
1
25.0
vi) 3
2
064.0
Homework: 1.5 # 6-9odd, 10a-d, 11odd