Indices is a number with the power. For example: a^{m}; 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
Any number, except 0, whose index is 0 is always equal to 1.
An example:
2° = 1
An example:
2^{-3 }= \(\frac{1}{2^3}\) ( using a^{-m }= \(\frac{1}{a^m}\))
In case of multiplication of same base, copy the base and add the indices.
An example:
3^{2 }x 3^{4} = 3^{2+4 }(using a^{m} x a^{n }= a^{ m+n})
= 3^{6}
= 3 x 3 x 3 x 3 x 3 x 3
= 729
In case of division of same base, copy the base and subtract the indices.
An example:
w^{10 }÷ w^{6}= w^{10-6} = w^{4}
To raise an expression to the n^{th} index, Copy the base and multiply the indices.
An example:
( x^{2})^{4} = x^{2x4 }= x^{8}
An example:
125^{\(\frac{2}{3}\) }= (\(\sqrt[3]{125}\))^{2} = (5)^{2} = 25
Solution,
(x^{3}y)×(xy)×(x^{2}y)
= x^{3}× x× x^{2}×y×y×y
=x^{3+1+2}×b^{1+1+1}
= x^{6}y^{3}
Solution:
\(\frac{-36a^8}{9a^5}\)
=\(\frac{-4×9a^{8-5}}{9}\)
= -4a^{3}
Solution:
(a^{2}b)×(ab)
=a^{2}×a×b×b
=a^{2+1}×b^{1+1}
=a^{3}b^{2}
Solution:
(-7p^{3})^{4}
=(-7)^{4}.(p^{3})^{4}
=7^{4}.p^{3×4}
=7^{4}p^{12}
Solution:
(xy^{2})^{3}×xy
=x^{3}(y^{2})^{3}×xy
=x^{3}y^{2×3}×xy
=x^{3}.x.y^{6}.y
=x^{3+1}.y^{6+1}
=x^{4}y^{7}
Solution:
(4x^{4})×(3x^{3})^{4}=4^{3}(x^{4})^{3}×3^{4}(x^{3})4
=4^{3}.x^{4×3}.3^{4}.x^{3×4}
=64×81.x^{12}.x^{12}
=4^{3}×3^{4}x^{12+12}
=4^{3}×3^{4} x^{24}
Solution:
\(\frac{(3p^2q)^2}{p^2q^2}\)
\(\frac{3^2(p^2)^2.q^2}{9p^2q^2}\)
=\(\frac{9p^4.q^2}{9p^2q^2}\)
=p^{4-2}q^{2-2}
=p^{2}.q^{0}
=p^{2}
Solve the following question by using the law of indices:
- 125 p^{7} (div)(-25p^{6})
Solve, by using the law of indices:
8^{4}( imes) 8^{3}
Solve, by using the law of indices:
(3x^{3}) ( imes)(2x^{2})
Solve, by using the law of indices:((frac{xy^2}{y^3}))^{2}
Solve, by using the law of indices:
(frac{2^3 imes4^2}{8^2})
Solve, by using the law of indices:
(frac{a^m+n+2 imes a^m+n+2}{a^m+n})
Find the value, by using the law of indices:
(a^{2}b)^{c}( imes)(ab^{2})^{c}
Find the value, by using the law of indices:
3^{5}(div)3^{3}
Find the value, by using the law of indices:
-36a^{8} (div) 9a^{5}
Find the value, by using the law of indices:
(xy^{-2}) ( imes)(-3y^{4})
Find the value, by using the law of indices:
(4x^{4})^{3} ( imes)(3x^{3})^{4}
Find the value, by using the law of indices:
12x^{7} (div) 3x^{5}
Find the value, by using the law of indices:
(a^{3}b)( imes)(ab) ( imes)(a^{2}b)
Find the value, by using the law of indices:
(frac{5^3 imes 125^3}{23^3})
Find the value, by using the law of indices:
x^{6} ( imes) x^{7}
Two numbers are in the Ratio of 4:5.If the sum of two number is 981. Find the value.
Solve:
(frac{3x+3}{4x-4}) = (frac{3}{4})
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