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The Laws of indices. Made by – Keval Ashar. Indices. exponent. base. 5 3 means 3 factors of 5 or 5 x 5 x 5. The Laws of indices :. #1: The exponent of a power indicates how many times the base multiplies itself. n factors of x. - PowerPoint PPT Presentation
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Made by – Keval Ashar
Indices Indices
35base
exponent
3 3 means that is the exponential
form of t
Example:
he number
125 5 5
.125
53 means 3 factors of 5 or 5 x 5 x 5
The Laws of indices :The Laws of indices :
#1: The exponent of a power indicates how many times the base multiplies itself.
n
n times
x x x x x x x x
3Example: 5 5 5 5
n factors of x
#2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS!
m n m nx x x
So, I get it! When you multiply Powers, you add the exponents!
512
2222 93636
#3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS!
mm n m n
n
xx x x
x
So, I get it!
When you divide Powers, you subtract the exponents!
16
222
2 4262
6
Try these:
22 33.1
42 55.2
25.3 aa
72 42.4 ss
32 )3()3(.5
3742.6 tsts
4
12
.7s
s
5
9
3
3.8
44
812
.9ts
ts
54
85
4
36.10
ba
ba
22 33.1 42 55.2 25.3 aa
72 42.4 ss
32 )3()3(.5
3742.6 tsts
8133 422
725 aa
972 842 ss
SOLUTIONS
642 55
243)3()3( 532
793472 tsts
4
12
.7s
s
5
9
3
3.8
44
812
.9ts
ts
54
85
4
36.10
ba
ba
SOLUTIONS
8412 ss
8133 459
4848412 tsts
35845 9436 abba
#4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents!
nm mnx x
So, when I take a Power to a power, I multiply the exponents
62323 55)5(
#5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent.
n n nxy x y So, when I take a Power of a Product, I apply the exponent to all factors of the product.
222)( baab
#6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent.
n n
n
x x
y y
So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.
81
16
3
2
3
24
44
Try these:
523.1
43.2 a
322.3 a
23522.4 ba
22 )3(.5 a
342.6 ts
5
.7t
s
2
5
9
3
3.8
2
4
8
.9rt
st
2
54
85
4
36.10
ba
ba
523.1
43.2 a
322.3 a
23522.4 ba
22 )3(.5 a
342.6 ts
SOLUTIONS
10312a
6323 82 aa
6106104232522 1622 bababa
4222 93 aa
1263432 tsts
5
.7t
s
2
5
9
3
3.8
2
4
8
.9rt
st
2
54
85
4
3610
ba
ba
SOLUTIONS
62232223 8199 babaab
2
8224
r
ts
r
st
824 33
5
5
t
s
#7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent.
1mm
xx
So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent.
Ha Ha!
If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!
933
1
125
1
5
15
22
33
and
#8: Zero Law of Exponents: Any base powered by zero exponent equals one.
0 1x
1)5(
1
15
0
0
0
a
and
a
and
So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.
Try these:
022.1 ba
42.2 yy
15.3 a
72 4.4 ss
4323.5 yx
042.6 ts
122
.7x
2
5
9
3
3.8
2
44
22
.9ts
ts
2
54
5
4
36.10
ba
a
SOLUTIONS
022.1 ba
15.3 a
72 4.4 ss
4323.5 yx
042.6 ts
1
5
1
a54s
12
81284
813
y
xyx
1
122
.7x
2
5
9
3
3.8
2
44
22
.9ts
ts
2
54
5
4
36.10
ba
a
SOLUTIONS
4
41x
x
8
824
3
133
44222 tsts
2
101022
819
a
bba