Question

Use rational exponents to simplify the expression. If rational exponents appear after​ simplifying, write the answer in radical notation. Assume that all variables represent positive numbers.
RootIndex 12 StartRoot left parenthesis 5 y right parenthesis Superscript 4 EndRoot
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Part 1
RootIndex 12 StartRoot left parenthesis 5 y right parenthesis Superscript 4 EndRootequals
  
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Answer 1

To simplify the expression \( \sqrt[12]{(5y)^4} \) using rational exponents, we first express the root using a rational exponent:

\[
\sqrt[12]{(5y)^4} = (5y)^4^{1/12}
\]

This can be simplified further by multiplying the exponents:

\[
(5y)^{4 \cdot \frac{1}{12}} = (5y)^{\frac{4}{12}} = (5y)^{\frac{1}{3}}
\]

Next, we can convert this back to radical notation:

\[
(5y)^{\frac{1}{3}} = \sqrt[3]{5y}
\]

Thus, the simplified expression in radical notation is:

\[
\sqrt[3]{5y}
\]