Verified answer

When multiplying exponents, you add them.

Therefore: 4m^-15/4 * m^15/4 = 4

Since: -15/4 + 15/4 = 0 ==> m^0 = 1 ==> 4 * 1 = 4

The exponents in the second half of the equation 4m^-15/4 * m^1/4 :

-15/4 + 1/4 = -14/4 ==> m^-14/4 *4 = 4/m^14/4

m^14/4 is written under the 4 because it is negative. It is the same as 4m^-14/4.

Therefore the answer would be 4 + 4/m^14/4.

I do not know how you're getting 4 + 4/m^4 unless you have the equation written wrong and it is actually:

4m^-15/4 (m^15/4+m^-1/4)

Hope that was helpful.