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Exponents And Powers

Question

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Find the value of m when $fraction numerator 5 to the power of straight m plus 5 to the power of negative 3 end exponent over denominator 5 squared end fraction space equals space 5 cubed$

Solution

We have
          $fraction numerator 5 to the power of straight m plus 5 to the power of negative 3 end exponent over denominator 5 squared end fraction space equals space 5 cubed$
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$rightwards double arrow$                       $5 to the power of straight m minus 5 end exponent space equals space 5 cubed$
   Since base is same on both sides, their exponents are same

∴                  m - 5 = 3
$rightwards double arrow$                     m = 3 + 5 = 8

       Thus, the required value of m is 8.

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