Question

Can someone please demonstrate how to turn a radical expression into an exponent expression? And then how to turn an exponent expression into a radical expression? Please and thanks so much!

Answer 1

I know how to simplify a radical expression, but that is about it. I am completely lost here, and have to answer this question for school today, so if someone could please help me I would greatly appreciate it. Thanks.

Answer 2

\[\Large \left(\sqrt[m]{x}\right)^n=\sqrt[m]{x^n}= x^{\frac{n}{m}}\]

Answer 3

example:
\[\Large \left(\sqrt[3]{125}\right)^7=\sqrt[3]{125^7}= 125^{\frac{7}{3}}\]

Answer 4

In the "special" case where there is no number "in" the square root:
\[\Large \sqrt{x}=x^{\frac{1}{2}} \]

Answer 5

So if that is how to turn a radical expression into an exponent expression, then how do we turn an exponent expression into a radical expression?

Answer 6

It's the same, just go in reverse.
\[\Large x^{\frac{n}{m}}=\sqrt[m]{x^n}=\left(\sqrt[m]{x}\right)^n \]

Answer 7

Thank you!