Question 845263
First, let's review some basic algebra principles. We know that 

a^1/n = nth root (a) 

For example, a^1/2 = sqrt(a).

So, we can rewrite this equation like this:

7throot(2m+4) - 7throot(m-3) = 0

Now, to get rid of roots, we simply need to raise the expression to the same power as the root, in this case 7. 

(7throot(2m+4))^7 - (7throot(m-3))^7 = (0)^7.

We are then left with 

2m+4 - m - 3 = 0

Now let's solve for m.

Combine like terms

(2m)-m + 4 - 3 = 0


 and we are left with


m + 1 = 0. 

Therefore m = -1.