When a number, variable, or expression is raised to a power, the number, variable, or expression is...
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![Page 1: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/1.jpg)
![Page 2: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/2.jpg)
When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.
nb
![Page 3: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/3.jpg)
An exponent means that you multiply the base by itself that many times.
For example
xx4 4 = = x x ● ● xx ●● xx ●● xx
226 6 = = 2 2 ● ● 22 ● ● 22 ● ● 22 ● ● 22 ● ● 22 = 64= 64
![Page 4: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/4.jpg)
When an expression does not have a visible exponent its exponent is understood to be 1.
1xx
![Page 5: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/5.jpg)
When multiplying two expressions with the same base you add their exponents.
For example
mn bb mnb
42 xx 42x 6x 222 21 22 212 32 8
![Page 6: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/6.jpg)
Try it on your own: mn bb mnb
73.1 hh33.2 2
1073 hh
312 33
27333
![Page 7: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/7.jpg)
When dividing two expressions with the same base you subtract their exponents.
For example
m
n
bb mnb
2
4
xx
24x 2x
![Page 8: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/8.jpg)
Try it on your own:
m
n
bb mnb
2
6
.3hh
33.4
3
26h 4h
133 23 9
![Page 9: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/9.jpg)
When raising a power to a power you multiply the exponents
For example
mnb )( mnb 42 )(x 42x 8x
22 )2( 222 42 16
![Page 10: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/10.jpg)
Try it on your own
mnb )( mnb
23)(.5 h 23h 6h22 )3(.6 223 43 81
![Page 11: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/11.jpg)
When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction
222 )2( x 44 2xYou would have to use FOIL in these cases
![Page 12: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/12.jpg)
When a product is raised to a power, each piece is raised to the power
For example
mab)( mmba
2)(xy 22 yx2)52( 22 52 254 100
![Page 13: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/13.jpg)
Try it on your own
mab)( mmba3)(.7 hk 33kh
2)32(.8 22 32 94 36
![Page 14: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/14.jpg)
This rule is for products only. When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction
2)2( x 22 2xYou would have to use FOIL in these cases
![Page 15: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/15.jpg)
When a quotient is raised to a power, both the numerator and denominator are raised to the power
For example
m
ba
m
m
ba
3
yx
3
3
yx
![Page 16: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/16.jpg)
Try it on your own
m
ba
m
m
ba
2
.9kh
2
2
kh
2
24.10 2
2
24
416
4
![Page 17: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/17.jpg)
When anything, except 0, is raised to the zero power it is 1.
For example0a 1 ( if a ≠ 0)
0x 1 ( if x ≠ 0)
025 1
![Page 18: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/18.jpg)
Try it on your own0a 1 ( if a ≠ 0)
0.11 h 1 ( if h ≠ 0)
01000.12 100.13 0
![Page 19: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/19.jpg)
If b ≠ 0, then
For example nb nb
1
2x 2
1x
23 231
91
![Page 20: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/20.jpg)
If b ≠ 0, then
Try it on your own: nb nb
1
3.14 h 3
1h
32.15 321
81
![Page 21: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/21.jpg)
The negative exponent basically flips the part with the negative exponent to the other half of the fraction.
2
1b
1
2b 2b
2
2x
12 2x 22x
![Page 22: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/22.jpg)
For a problem to be completely simplified there should not be any negative exponents
![Page 23: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/23.jpg)
9
5
36.1dd 952 d 42 d 4
2d
54 42.2 ee 548 e 98e
![Page 24: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/24.jpg)
54.3 q 54q 20q
52.4 lp 5552 pl 5532 pl
![Page 25: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/25.jpg)
2
42
)()(.5
xyyx
22
48
yxyx
2428 yx 26 yx
9
253 )(.6xxx
9
28 )(xx
9
16
xx
916x 7x
![Page 26: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/26.jpg)
6523246 )()(.7 pnmnm301218812 pnmnm
301281812 pnm 302030 pnm
![Page 27: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/27.jpg)
4
6
)2()2(.8yxyx
46)2( yx 2)2( yx
)2)(2( yxyx
F2x
Oxy2
Ixy2L
24y22 44 yxyx
![Page 28: When a number, variable, or expression is raised to a power, the number, variable, or expression is called the base and the power is called the exponent.](https://reader034.fdocuments.us/reader034/viewer/2022052514/5a4d1af37f8b9ab05997f4cb/html5/thumbnails/28.jpg)
94
56
.9dada 9546 da 42 da
4
2
da