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Note on Law of Indices

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  • Note
  • Things to remember
  • Exercise
  • Quiz

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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%
  • Solve the following question by using the law of indices:

    - 125 p7 (div)(-25p6)

    7p
    6p
    5p
    10p
  • Solve, by using the law of indices:

    84( imes) 83

    87
    88
    83
    85
  • Solve, by using the law of indices:

    (3x3) ( imes)(2x2)

    6x4
    6x8
    6x7
    6x5
  • Solve, by using the law of indices:((frac{xy^2}{y^3}))2

    x2
    7xy2
    x2y 
    x2y2
  • Solve, by using the law of indices:

    (frac{2^3 imes4^2}{8^2})

    5
    2
    7
    3
  • Solve, by using the law of indices:

    (frac{a^m+n+2 imes a^m+n+2}{a^m+n})

    am+n+3
    am+n+1
    am+n+4
    am+n+2
  • Find the value, by using the law of indices:

    (a2b)c( imes)(ab2)c

    a3c.b3c
    ac.ac
    a2c.a2c
    a5c.a5c
  • Find the value, by using the law of indices:

    35(div)33

    9
    7
    11
    8
  • Find the value, by using the law of indices:

    -36a8 (div) 9a5

    5a3
    4a3
    -5a3
    -4a3
  • Find the value, by using the law of indices:

    (xy-2) ( imes)(-3y4)

    3xy2
    -2xy2
    -5xy2
    -3xy2
  • Find the value, by using the law of indices:

    (4x4)3 ( imes)(3x3)4

    43( imes) 34 x24
    45( imes) 34 x24
    42( imes)33 x24
    43( imes)34 x25
  • Find the value, by using the law of indices:

    12x7 (div) 3x5

    5x2
    3x2
    7x2
    4x2
  • Find the value, by using the law of indices:

    (a3b)( imes)(ab) ( imes)(a2b)

    a7b3
    a5b3
    a6b3
    a3b3
  • Find the value, by using the law of indices:

    (frac{5^3 imes 125^3}{23^3})

    55
    56
    57
    58
  • Find the value, by using the law of indices:

    x6 ( imes) x7

    x13
    x12
    x10
    x15
  • Two numbers are in the Ratio of 4:5.If the sum of two number is 981. Find the value.

    435, 550
    436, 545
    430, 540
    437, 500
  • Solve:

    (frac{3x+3}{4x-4}) = (frac{3}{4})

    x=7
    x=8
    x=4
    x=5
  • You scored /17


    Take test again

DISCUSSIONS ABOUT THIS NOTE

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Forum Time Replies Report
X^2 x÷x

X^2x÷x


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for Dle plz

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


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aligit k m

if log2^k〓4, what is the value of k?


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kareem azeezat

Ask any queries on this note.2:3÷3:5


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