By: Jeffrey Bivin Lake Zurich High School [email protected] Last Updated: October 30, 2006.
Rational Expon ents and Radicals By: Jeffrey Bivin Lake Zurich High School Last Updated: December...
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Transcript of Rational Expon ents and Radicals By: Jeffrey Bivin Lake Zurich High School Last Updated: December...
Rational Exponents
and
RadicalsBy: Jeffrey Bivin
Lake Zurich High School
Last Updated: December 11, 2007
Properties of rational Exponentsn aa n
1
mnnm
aa1
mn a
n ma nnm maa
1
21616 441
821616 33443
840961616 44 343
n mmn aa
Jeff Bivin -- LZHS
Are these equivalent?
77 xx
533 5 xx
353 5 xx
73 53 75 xx Jeff Bivin -- LZHS
Evaluate each
xx 2
xx 3 3
xx 4 4
xx 5 5
xx 6 6
Jeff Bivin -- LZHS
Evaluate7x
xxxx 222
xxxx 222
xxxx
xx3
Jeff Bivin -- LZHS
Now Consider7x
xx 32
xx 32
xx 3
2
xxxx 222
xx3
n mmn aa
Jeff Bivin -- LZHS
Evaluate3 14x
3 23333 xxxxx
3 23 33 33 33 3 xxxxx
3 2xxxxx
3 24 xx
Jeff Bivin -- LZHS
Consider3 14x
3 24 xx
3 243 xx
3 24
3 3 xx 3 23 33 33 33 3 xxxxx
3 23333 xxxxx
3 14x
3 2xxxxx 3 24 xx
Jeff Bivin -- LZHS
One More3 14x
314
x3 212 xx
3 23 12 xx
32
312
xx
3 14x
324 xx
3 24 xx3 24 xx
Jeff Bivin -- LZHS
Evaluate5 332614 zyx
5 365155425 zzyyxx
5 34652 zyxzyx
5 3146
5 55
5 52
5 5 zyxzyx
Jeff Bivin -- LZHS
Evaluate5 332614 zyx
5 34652 zyxzyx
Jeff Bivin -- LZHS
Evaluate7 231434 zyx
7 26324 zxzyx
Jeff Bivin -- LZHS
Evaluate4 291815 zyx
4 23743 zyxzyx
4 23734 zyxzxy
Don’t forget, even root – we
need to use absolute value
An even power can
come out of the absolute
value
Jeff Bivin -- LZHS
Evaluate: 3 144
3 211 322
144
722
9832 23
3 24 32
3 182Jeff Bivin -- LZHS
Evaluate: 4000
1112 5252
4000
10040
10422 52
35 52
1020
21022 52
Jeff Bivin -- LZHS
Evaluate: 2791152 yx
yxyx 113413 232
1152
5762
2
1442
27927 32 yx
xyyx 224 134
288
212
222 32 42
Jeff Bivin -- LZHS
5 1419612 32 ba
5 1175 312 5832512 baba
5 1419639 322 ba
Simplify
5 44122312 3232 baba
5 4423 1212 babaJeff Bivin -- LZHS
53233
1523
Simplify
5363563
Jeff Bivin -- LZHS
3 43 3 22
3 223 2 2222
Simplify
33333 4424424
3 222
Jeff Bivin -- LZHS
Simplify
5337
57355432
Jeff Bivin -- LZHS
253916269233622
Simplify
359246233262
34523
759326183722
34522429212
Jeff Bivin -- LZHS
Simplify
3 1083 3 )108()1(
108
542
9623
Jeff Bivin -- LZHS
32
3 1083 32 32
33 2 4323
Jeff Bivin -- LZHS
Simplify
22
42
22
21
21
Jeff Bivin -- LZHS
Simplify
326
26
Jeff Bivin -- LZHS
330
930
33
310
310
Simplify
Jeff Bivin -- LZHS
55
532
512
512
1024
1024
Simplify
5152
25152
Jeff Bivin -- LZHS
24
22
22
22
21
21 33 2
3 3
3 2
3 2
3 2
33
Simplify
Jeff Bivin -- LZHS
3162
332
33
32
32 5
5 5
5 4
5 4
5 4
5
55
Simplify
Jeff Bivin -- LZHS
zyzyx
zy
zyx 6 24
6 66
6 24
6 24
6 24
6 42
6
642
zy
zy
zy
xzyx
Simplify
Jeff Bivin -- LZHS
220
2
25 5
5 5
5 2
5 2
5 2
5 3
55
2
2
2
585
Simplify
Jeff Bivin -- LZHS
48
22
22
22
21
321 4
2
4 3
4 8
4 3
4 3
4 3
4 54
Simplify
Jeff Bivin -- LZHS
Express using Rational Exponents
21
77 51
225
323 2 xx
Jeff Bivin -- LZHS
Express using Rational Exponents
23
696 9 aaa
Jeff Bivin -- LZHS
Express using Rational Exponents
8 6524 yx
86
85
81
83
32 yx 43
8 653 32 yx
Jeff Bivin -- LZHS
Express in Simplest Radical From
52
x 5 2x
Jeff Bivin -- LZHS
Express in Simplest Radical From
32
64 3 264
3 262
1622 43 12
Jeff Bivin -- LZHS
Express in Simplest Radical From
47
x4 7x4 3xx
Jeff Bivin -- LZHS
Express in Simplest Radical From
310
35
yx
31105 yx3 233 105 yxyxyx
Jeff Bivin -- LZHS
Express in Simplest Radical From
27
45
32
zyx1242
1215
128
zyx12 638312 42158 zyxzyzyx
Jeff Bivin -- LZHS
Express in Simplest Radical From
3 2616 yx
2131
2616 yx 612616 yx
6 2616 yx 6 2442 yxyx
2
Jeff Bivin -- LZHS
Express in Simplest Radical From
41
31
21
2110
yx
24 2110 yx
Jeff Bivin -- LZHS
2412110 yx
4 3 2110 yx
Express in Simplest Radical From
5 11375 yxyx
5121
11375 yxyx
1012113575 yxyx
105
102
Express in Simplest Radical From
1012113575 yxyx
1012263525 yxyx10 5731 yx 10 7153 yxyx
Express in Simplest Radical From
5 11375 yxyx
10 22610 3525 yxyx
10 2263525 yxyx10 7153 yxyx
Express in Simplest Radical From
12 5 21122110 yxyx
Jeff Bivin -- LZHS
4 33
5 742110 yxyx
12 10 422410550 yxyx
2
120 14774 yx 120 2774 yxy
Express in Simplest Radical From
21
126
xx
Jeff Bivin -- LZHS
x
12 6x
4 32 zyx
Express in Simplest Radical From
Jeff Bivin -- LZHS
8 624 zyx
Express in Simplest Radical From
Jeff Bivin -- LZHS
12 694 zyx
12 694 zyx
6 2442 yxyx
3 242 yxyx
Express in Simplest Radical From
Jeff Bivin -- LZHS
Express in Simplest Radical From
Jeff Bivin -- LZHS
6 246 yx
6 246 yx
Express in Simplest Radical From
Jeff Bivin -- LZHS
3 1222 yx3 24 yx
6 2416 yx remember
16 = 24
6 2442 yx
723
223239
232323
231
Simplify
Jeff Bivin -- LZHS
11
531211543
5545416
5435454
543
Simplify
Jeff Bivin -- LZHS
371
6712
7771
7127171
712
Simplify
Jeff Bivin -- LZHS
3321332
332324
3323232
323
Simplify
Jeff Bivin -- LZHS