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