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Exponents And Powers

Question
CBSEENMA8002645
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Find the value of m for which 5 to the power of straight m space divided by space 5 to the power of negative 3 end exponent space equals space 5 to the power of 5.

Solution

∵    straight a to the power of straight m space divided by space straight a to the power of straight n space equals space straight a to the power of straight m minus straight n end exponent

∴     L.H.S = 5 to the power of straight m space divided by space 5 to the power of negative 3 end exponent
 
             = 5 to the power of straight m minus left parenthesis negative 3 right parenthesis end exponent space equals space 5 to the power of straight m plus 3 end exponent
Now,     5 to the power of straight m plus 3 end exponent space equals space 5 to the power of 5
   Since, bases 5 are equal, therefore exponents are also equal.
i.e.         m + 3 = 5
or                      m = 5 -3 = 2
  Thus, the required value of m is 2.

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