m^{-7 - (-5)}  = m^{-7  +  (+5)} = m ^-2 = 1/m²

     m^-7/m^-5  by definition of negative exponents m^-7  =  1/m⁷  and m ^-5   =  1/m⁵  So we substitute them  into the fraction m^-7/m^-5 = 1/m⁷ /  1/m⁵ . 

This symbol / tells us that this is is a division problem so 1/m⁷ /  1/m ⁵  =    1/m⁷ ÷ 1/m⁵  = 

    1/m⁷ x m ⁵ /1  =  m ⁵ / m⁷  = m ^{5 - 7} = m ^-2  = 1/ m ²  Notice that a lot of this work is from basic math.

You can eliminate a lot of these steps by remembering that whenever you

 move a term from the denominator to the numerator or vice versa the sign

 of the exponent changes.  So we could have gone from m^-7/m ^-5  directly

to m ⁵ / m⁷ and avoided the above steps. Then the solution would be m⁵ / m⁷  = m ^{5 - 7} = 

                                                                                                                                                                   m ^-2 = 1/m ²           

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