1 rules for exponents
TRANSCRIPT
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When you multiply like variables you ADD their exponents
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When you multiply like variables you ADD their exponents
- When you divide like variables you SUBTRACT their exponents
![Page 4: 1 rules for exponents](https://reader033.vdocuments.us/reader033/viewer/2022042510/55844a8bd8b42af85e8b4a0c/html5/thumbnails/4.jpg)
Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When you multiply like variables you ADD their exponents
- When an exponent is raised to another exponent, you MULTIPLY exponents
- When you divide like variables you SUBTRACT their exponents
![Page 5: 1 rules for exponents](https://reader033.vdocuments.us/reader033/viewer/2022042510/55844a8bd8b42af85e8b4a0c/html5/thumbnails/5.jpg)
Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When you multiply like variables you ADD their exponents
- When an exponent is raised to another exponent, you MULTIPLY exponents
- When you divide like variables you SUBTRACT their exponents
- When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.
![Page 6: 1 rules for exponents](https://reader033.vdocuments.us/reader033/viewer/2022042510/55844a8bd8b42af85e8b4a0c/html5/thumbnails/6.jpg)
Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When an exponent is raised to another exponent, you MULTIPLY exponents
- When you divide like variables you SUBTRACT their exponents
- When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.
75252 xxxx
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When an exponent is raised to another exponent, you MULTIPLY exponents
- When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.
75252 xxxx
3585
8
xxx
x
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
- When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.
75252 xxxx
3585
8
xxx
x
124343 xxx
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
75252 xxxx
3585
8
xxx
x
124343 xxx
33 1
xx
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Algebraic Expressions – Rules for Exponents
Let’s review the rules for exponents you learned in Algebra 1 :
n
n
nmnm
nmn
m
nmnm
aa
aa
aa
a
aaa
1
75252 xxxx
3585
8
xxx
x
124343 xxx
33 1
xx
What we are going to do in Pre – Calc is take these rules and combine them into multi – step problems that might have all four rules utilized.
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
Since everything is multiplied, we can multiply all integers, and all like variables.
cba
cbbaa
2231
223
8
42
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
Example # 2 :935236 xxxx nnmm
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
Example # 2 :935236 xxxx nnmm
Don’t PANIC !!! The rule for multiplying like variables still applies. Exponents can be algebraic, integers, or fractions
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
Example # 2 :935236 xxxx nnmm
Don’t PANIC !!! The rule for multiplying like variables still applies. Exponents can be algebraic, integers, or fractions
935236 xxxx nm We will still ADD exponents
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Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
Example # 2 :935236 xxxx nnmm
Now just treat the exponent like an algebraic expression where we combine like terms…
462
935236
xx
xxxx
nm
nm We will still ADD exponents
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
When you have imbedded parentheses and exponents outside, start with the innermost set and work your way “out”.
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
Evaluate this first, applying the exponent outside to ALL of the terms inside.
3 2322224 yx
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
3 64
3 23222
44
24
yx
yx
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
I like to multiply what is inside the brackets before I apply the outside exponent.
3 64
3 64
3 23222
16
44
24
yx
yx
yx
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
Apply the outside exponent.
36343
3 64
3 64
3 23222
16
16
44
24
yx
yx
yx
yx
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Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
181218123
36343
3 64
3 64
3 23222
4096or 16
16
16
44
24
yxyx
yx
yx
yx
yx
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Algebraic Expressions – Rules for Exponents
Example # 4 :5
23
6
3
ab
ba There are two ways to attack this problem.
1. Apply the division rule using negative exponents.
2. Use the negative exponent rule first, then apply the division rule.
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Algebraic Expressions – Rules for Exponents
Example # 4 :5
23
6
3
ab
ba There are two ways to attack this problem.
1. Apply the division rule using negative exponents.
2. Use the negative exponent rule first, then apply the division rule.
32
5213
2
16
3
ba
ba
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Algebraic Expressions – Rules for Exponents
Example # 4 :5
23
6
3
ab
ba There are two ways to attack this problem.
1. Apply the division rule using negative exponents.
2. Use the negative exponent rule first, then apply the division rule.
2
53
6
3
ab
ba
I applied the negative exponent rule and moved any variable with a negative exponent to the other part of the fraction and made the exponent positive…
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Algebraic Expressions – Rules for Exponents
Example # 4 :5
23
6
3
ab
ba There are two ways to attack this problem.
1. Apply the division rule using negative exponents.
2. Use the negative exponent rule first, then apply the division rule.
32
2513
2
53
2
16
36
3
ba
ba
ab
ba
Apply the normal division of like variables rule…
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Algebraic Expressions – Rules for Exponents
Example # 5 : 3
1
21
21
43
236
yx
yx This problem has a few rules to apply, apply the exponent to each parentheses first…
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Algebraic Expressions – Rules for Exponents
Example # 5 : 3
1
21
21
43
236
yx
yx This problem has a few rules to apply, apply the exponent to each parentheses first…
34
41
31
31
21
21
21
21
63643
2
xy
xy
yx
yx
When you have an integer to the ½ power, it is the square root of the integer.
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Algebraic Expressions – Rules for Exponents
Example # 5 : 3
1
21
21
43
236
yx
yx This problem has a few rules to apply, apply the exponent to each parentheses first…
34
41
34
41
31
31
21
21
21
21
11
43
2
6
636
yx
xy
xy
yx
yx
Now you divide your variables…
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Algebraic Expressions – Rules for Exponents
Example # 5 : 3
1
21
21
43
236
yx
yx This problem has a few rules to apply, apply the exponent to each parentheses first…
1213
1213
34
41
34
41
31
31
21
21
21
21
66
6
636
11
43
2
yy
yx
xy
xy
yx
yx
Anything to the zero power = 1, and it is not necessary to change improper fractions to mixed numbers…
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Algebraic Expressions – Rules for Exponents
Example # 6 :1
213
532
4
12
zyx
zyx
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Algebraic Expressions – Rules for Exponents
Example # 6 :1
213
532
4
12
zyx
zyx On this one I would reduce any integer fraction first…
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Algebraic Expressions – Rules for Exponents
Example # 6 :
1
213
532
1
213
532
3
4
12
zyx
zyx
zyx
zyx On this one I would reduce any integer fraction first…
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Algebraic Expressions – Rules for Exponents
Example # 6 :
213
5321
121113
1513121
1
213
532
1
213
532
3
3
3
4
12
zyx
zyx
zyx
zyx
zyx
zyx
zyx
zyx
Now apply the negative exponent outside…
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Algebraic Expressions – Rules for Exponents
Example # 6 :
231
532
213
5321
121113
1513121
1
213
532
1
213
532
3
3
3
3
4
12
zyy
zxx
zyx
zyx
zyx
zyx
zyx
zyx
zyx
zyx
Move your negative exponent variables…
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Algebraic Expressions – Rules for Exponents
Example # 6 :
231
532
213
5321
121113
1513121
1
213
532
1
213
532
3
3
3
3
4
12
zyy
zxx
zyx
zyx
zyx
zyx
zyx
zyx
zyx
zyx
Apply multiplication and division of variables rules…
4
35
31
2532
33 y
zx
y
zx