Law of Indices | kullabs.com

## Note on Law of Indices

• Note
• Things to remember
• Exercise
• Quiz

Indices is a number with the power. For example: am; a is called the base and m is the power. These laws only apply to expression with the same base.

Index help to write a product of numbers very compactly. Index help to show how many times to use the number in a multiplication. It is shown in the top right of the number in small number.

In this example: 4³ = 4x4x4 = 64

### Rule1: a° = 1

Any number, except 0, whose index is 0 is always equal to 1.

An example:

2° = 1

### Rule 2: a-m = $$\frac{1}{a^m}$$

An example:

2-3 = $$\frac{1}{2^3}$$ ( using a-m = $$\frac{1}{a^m}$$)

### Rule 3: amx an = am+n

In case of multiplication of same base, copy the base and add the indices.

An example:

3x 34 = 32+4 (using am x a= a m+n)

= 36

= 3 x 3 x 3 x 3 x 3 x 3

= 729

### Rule 4: am ÷ an = am-n

In case of division of same base, copy the base and subtract the indices.

An example:

w10 ÷ w6= w10-6 = w4

### Rule 5: ( am)n = amn

To raise an expression to the nth index, Copy the base and multiply the indices.

An example:

( x2)4 = x2x4 = x8

### Rule 6: a$$\frac{m}{n}$$ = ($$\sqrt[n]{a}$$)m

An example:

125$$\frac{2}{3}$$ = ($$\sqrt[3]{125}$$)2 = (5)2 = 25

• An indices is a number with the power.
• The laws of indices state a number of rules, which can be used  to simplify expressions involving indices.
• Any number, except 0, whose index is 0 is always equal to 1. (i.e. a° = 1)
.

### Very Short Questions

Solution,

(x3y)×(xy)×(x2y)

= x3× x× x2×y×y×y

=x3+1+2×b1+1+1

= x6y3

Solution:

$$\frac{-36a^8}{9a^5}$$

=$$\frac{-4×9a^{8-5}}{9}$$

= -4a3

Solution:

(a2b)×(ab)

=a2×a×b×b

=a2+1×b1+1

=a3b2

Solution:

(-7p3)4

=(-7)4.(p3)4

=74.p3×4

=74p12

Solution:

(xy2)3×xy

=x3(y2)3×xy

=x3y2×3×xy

=x3.x.y6.y

=x3+1.y6+1

=x4y7

Solution:

(4x4)×(3x3)4=43(x4)3×34(x3)4

=43.x4×3.34.x3×4

=64×81.x12.x12

=43×34x12+12

=43×34 x24

Solution:

$$\frac{(3p^2q)^2}{p^2q^2}$$

$$\frac{3^2(p^2)^2.q^2}{9p^2q^2}$$

=$$\frac{9p^4.q^2}{9p^2q^2}$$

=p4-2q2-2

=p2.q0

=p2

0%

10p
5p
6p
7p

88
83
87
85

6x4
6x5
6x8
6x7

x2y
x2
7xy2
x2y2

3
7
5
2

am+n+2
am+n+3
am+n+1
am+n+4

a5c.a5c
ac.ac
a2c.a2c
a3c.b3c

9
7
11
8

4a3
5a3
-5a3
-4a3

3xy2
-3xy2
-2xy2
-5xy2
• ### Find the value, by using the law of indices:(4x4)3 ( imes)(3x3)4

45( imes) 34 x24
43( imes)34 x25
43( imes) 34 x24
42( imes)33 x24

4x2
3x2
7x2
5x2

a5b3
a7b3
a6b3
a3b3

58
57
55
56

x12
x15
x13
x10

430, 540
435, 550
436, 545
437, 500

x=8
x=5
x=7
x=4
• ## You scored /17

Forum Time Replies Report

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