Product of base when exponent is same


 
 
Concept Explanation
 

Product of Base when Exponent is Same

x^{m}times y^{m}=(xtimes y)^{m}

Where x, y are non - zero rational numbers and m is any integer.

Illustration: Evaluate 7^{-3}times 8^{-3}

Solution:  Using the law x^{m}times y^{m}=(xtimes y)^{m}  , we have

               7^{-3}times 8^{-3}=(7times 8)^{-3}

                                       =(56)^{-3}

                                      =frac{1}{(56)^{3}}                                    left [ because x^{-m}=frac{1}{x^{m}} right ]

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Sample Questions
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Question : 1

Evaluate:

left ( frac{1}{7} right )^{6}timesleft ( frac{1}{13} right )^{6}timesleft ( frac{3}{5}right )^{6}

Right Option : D
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Explanation
Question : 2

Evaluate

left ( frac{-3}{8} right )^{-2}timesleft ( frac{2}{11} right )^{-2}

Right Option : B
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Explanation
Question : 3

Simplify left ( frac{x}{y} right )^{3}times ;left ( frac{y}{x} right )^{3}

Right Option : A
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Explanation
 
 
 
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