Question

in r^n=a then which of the following is true?
^nsqrta=r
a^1/n=r
n^1/r=a
a^r=n

Answer 1

I think what you wrote isn't what you meant to write...

I'll just give you the answer to illustrate what I mean:

Because math hierarchy places exponentiation above division,
a^1/n means essentially a/n because a^1 = a.

What you meant to write was a^(1/n) which in fact does equal the r in your example.

Answer 2

So you know that \(r^n=a\). Suppose you want to solve for r. Ycan do that by raising both sides to the power 1/n:
\[\left(r^n\right)^{\frac{1}{n}}=a^{\frac{1}{n}}\]Why would you do this?
Well, you know the rule \((a^b)^c=a^{bc}\), so if we apply this to our equation, we get on the left hand side:\[r^{n \cdot \frac{1}{n}}=r^{\frac{n}{n}}=r^1=r\]
So we have found: \(r=a^{\frac{1}{n}}\)

It is your second answer option.