review: laws of exponents questions q: 4 0 =? a: 1 q: 4 1 =? a: 4 q: 4 1/2 =? a: let’s square the...
TRANSCRIPT
Review: Laws of Exponentsnmnm aaa
nmn
m
aa
a
nmnm aa
n
nn
b
a
b
a
nnn baba )(
nn
aa
1
QuestionsQ: 40 =?A: 1
Q: 41 =?A: 4
Q: 41/2=? A: Let’s square the number (41/2)2 =?
(41/2)2 = 41 = 4
Recall: b is called a square root of the number a if b2 = a.
41/2 is a square root of the number 4
Or 4421
Definition of Rational Exponent
Q: 81/3=? A: Let’s cube the number (81/3)3 =?
(81/3)3 = 81 = 8So, we have
In general, for any positive integer n,
aa 2
1
33
1
88
nn aa 1
ExamplesEvaluate the following expressions
3
1
27
2
1
100
4
1
16
4
1
4
1
)16(
3
1
)8(
ExamplesSimplify the following expressions
4
4/1
2/1
n
m
44/1
42/1
)(
)(
n
m
)4()4/1(
)4()2/1(
n
m
nm2
1
2
n
m
33/123/1 )2( xyx 323/13/1 )2( yx
320 )2( yx 323 )(2 y 68y
n
m1
2
Question
4/316Which way do you prefer?
?8 3/2 23 8
3/123/2
23/13/2
)8(8
)8(8
or
22 4
3 64 43 28
4 316 = 34 16
Definition of Rational Exponent
The numerator m will the exponentThe denominator n will be the index of the radical
253/2 =
n mmnn
m
aaa
2532 33
)5(25 125
Examples
1007/2 =
(-27)2/3 =
3/2
n mmnn
m
aaa
10072 7100 710 000,000,10
2723 23 9
36
1
36
1 32
3
6
1
216
1
ExamplesSimplify the following expressions
5/31032a 5/3105/3 )()32( a 63
5 32 a
68a63)2( a
2/34 )4( c 2/342/3 )(4 c
)()4( 2
343
c 632 c 68c
ExamplesSimplify the following expressions
3/29368 cba 3/293/233/263/2 )()()()8( cba
62423 8 cba 6244 cba62422 cba
3/23)27( a 3/233/2
3/2
)()27(
1
a3/2
327
1
a
223 27
1
a
22)3(
1
a 29
1
a