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

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

List-â… (Uses Of Exponent Rules)  List-â…¡(Term With Different Base And Same Exponent)
(A) (a/b)^x (i) frac{1}{a^x}
(B) a^{(-x)}    (ii) frac{a^x}{b^x}
(C)  (ab)^{x} (iii) a^{x}b^{x}

                              

Right Option : B
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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

Simplify and express in exponential form: (5^4x^{10}y^5/ 5^4x^7y^4)

Right Option : A
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