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

Notes, Exercises, Videos, Tests and Things to Remember on Law of Indices

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• 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)
.

#### Click on the questions below to reveal the answers

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%

6p
5p
10p
7p

85
87
88
83

6x4
6x5
6x8
6x7

7xy2
x2y2
x2
x2y

2
5
7
3

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

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

7
9
11
8

5a3
4a3
-5a3
-4a3

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

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

3x2
5x2
7x2
4x2

a3b3
a5b3
a6b3
a7b3

58
55
57
56

x12
x15
x13
x10

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

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

## ASK ANY QUESTION ON Law of Indices

Forum Time Replies Report

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?