Finding the nth root of a value x is the same as raising x to the power 1/n.
Let r be the square root of x. Then, we have
r^2 = x
We want to express r in terms of x^m. Our equation becomes
(x^m)^2 = x
Knowing that we can multiply the powers gives
x^2m = x
Finally, comparing powers gives
2m = 1 => m = 1/2
So, in general, if r is the nth root of x, so that
r^n = x,
we find that m = 1/n by going through the same process.
Let r be the square root of x. Then, we have
r^2 = x
We want to express r in terms of x^m. Our equation becomes
(x^m)^2 = x
Knowing that we can multiply the powers gives
x^2m = x
Finally, comparing powers gives
2m = 1 => m = 1/2
So, in general, if r is the nth root of x, so that
r^n = x,
we find that m = 1/n by going through the same process.
