Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in...
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Transcript of Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in...
![Page 1: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/1.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
![Page 2: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/2.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
![Page 3: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/3.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 you divide like variables you SUBTRACT their exponents
![Page 4: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/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: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/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: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/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
![Page 7: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/7.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 a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.
75252 xxxx
3585
8
xxx
x
![Page 8: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/8.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 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
![Page 9: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/9.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
75252 xxxx
3585
8
xxx
x
124343 xxx
33 1
xx
![Page 10: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/10.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
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.
![Page 11: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/11.jpg)
Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
![Page 12: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/12.jpg)
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
![Page 13: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/13.jpg)
Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
![Page 14: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/14.jpg)
Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
44
2231
223
8
8
42
Example # 2 :935236 xxxx nnmm
![Page 15: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/15.jpg)
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
![Page 16: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/16.jpg)
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
![Page 17: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/17.jpg)
Algebraic Expressions – Rules for Exponents
Example # 1 : cbbaa 22342
cba
cba
cbbaa
45
2241
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
![Page 18: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/18.jpg)
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”.
![Page 19: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/19.jpg)
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
![Page 20: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/20.jpg)
Algebraic Expressions – Rules for Exponents
Example # 3 : 3 23224 yx
3 64
3 23222
44
24
yx
yx
![Page 21: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/21.jpg)
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
![Page 22: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/22.jpg)
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
![Page 23: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/23.jpg)
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
![Page 24: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/24.jpg)
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.
![Page 25: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/25.jpg)
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
![Page 26: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/26.jpg)
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…
![Page 27: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/27.jpg)
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…
![Page 28: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/28.jpg)
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…
![Page 29: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/29.jpg)
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.
![Page 30: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/30.jpg)
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…
![Page 31: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/31.jpg)
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…
![Page 32: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/32.jpg)
Algebraic Expressions – Rules for Exponents
Example # 6 :1
213
532
4
12
zyx
zyx
![Page 33: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/33.jpg)
Algebraic Expressions – Rules for Exponents
Example # 6 :1
213
532
4
12
zyx
zyx On this one I would reduce any integer fraction first…
![Page 34: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/34.jpg)
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…
![Page 35: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/35.jpg)
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…
![Page 36: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/36.jpg)
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…
![Page 37: Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :](https://reader035.fdocuments.net/reader035/viewer/2022081516/551aa2355503466b3a8b57a2/html5/thumbnails/37.jpg)
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