Notes on Law of Indices | Grade 8 > Compulsory Maths > Algebra | KULLABS.COM

• 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$$\frac{2}{3}$$ = ($$\sqrt{125}$$)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
7p
5p
6p

83
85
88
87

6x7
6x4
6x5
6x8

7xy2
x2y2
x2y
x2

5
7
2
3

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

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

9
7
11
8

5a3
-5a3
-4a3
4a3

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

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

5x2
4x2
7x2
3x2

a3b3
a5b3
a7b3
a6b3

57
55
56
58

x13
x12
x15
x10

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

x=7
x=5
x=8
x=4

## ASK ANY QUESTION ON Law of Indices

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X^2x÷x

##### for Dle plz

Solve:(3^(x 1) 3^x)/(2*3^x)

##### aligit k m

if log2^k〓4, what is the value of k?