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

If 7^{(x-y)} =343 and 7^{(x+y)} =2401, then x is equal to________.

 

Right Option : D
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Question : 3

Using laws of exponents, simplify and write the answer in exponential form:    frac{(3^2)^5}{3^4}

Right Option : C
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