Question 845263: Solve the equation:
(2m+4)^(1/7)-(m-3)^(1/7)=0
The Solution set is______.
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! 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.
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