Simplification of Exponents and Power


 
 
Concept Explanation
 

Simplification of Exponents and Power

To simplify the exponents, we have some laws. These laws together can be used to covert exponent in the simplest form.

1. a^{m}times a^{n}=a^{m+n}

2.  frac{a^{m}}{a^{n}}=a^{m-n}

3. frac{1}{a^{m}}=a^{-m}

4. frac{a^{m}}{a^{n}}=left ( frac{a}{b} right )^{m}

5. left ( a^{m} right )^{n}=a^{mn}=left ( a^{n} right )^{m}

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Sample Questions
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Question : 1

If (frac{2}{3})^{x}(frac{3}{2})^{2x}=frac{81}{16}   ,then x=

Right Option : C
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Question : 2

Match the following provided that a and b are any rational numbers different from zero and x, y are any rational numbers.

List I(Terms With Same Base Different Exponents) List-â…¡ (Uses Of Basic Exponent Rule)
(A) (a^x)^y    (i) a^{x-y}
(B) a^x÷ a^y (ii) a^{xy}
(C) a^x X a^y    (iii) a^{x+y}
Right Option : A
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Question : 3

Simplify and express in exponential form: ((3^2)^3times 2^6)times 5^6

Right Option : D
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