To rewrite \( 5\sqrt[3]{3} \) using a rational exponent, recall that the nth root can be expressed as a fractional exponent, where the numerator is 1 and the denominator is the root index.
So, the expression \( \sqrt[3]{3} \) can be rewritten as \( 3^{1/3} \).
Therefore, \( 5\sqrt[3]{3} \) can be expressed as:
\[ 5 \cdot 3^{1/3} \]
However, looking at the response options you provided, \( 5\sqrt[3]{3} \) can be rewritten as:
\[ 5^{1} \cdot 3^{1/3} \]
But none of the options directly represent this combination.
However, if we focus solely on \( \sqrt[3]{3} \), it would be:
- \( 3^{5/3} \) from option (B) is incorrect.
- \( 5^{1/3} \) or \( 5^{1} \) does not match either.
It seems the closest response that reflects the use of a rational exponent from the choices given is:
\[ 3^{5} , (\text{option D}) \text{ but } 5^{\frac{1}{3}}\text{ is not an option.} \]
Ultimately, regarding rewriting \( 5\sqrt[3]{3} \), check if the question is focused on strictly converting \( \sqrt[3]{3} \) into a rational exponent, focusing on the options truly represents what was asked.
- If strictly about \( \sqrt[3]{3} \), it would be
Correct Answer: \( 3^{\frac{1}{3}} \) (but not directly one of your options).
If this doesn't fully align with your needs in context, please ensure to clarify the expressions at hand or any additional context they would have.
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