Question
According to exponent rules, what is the rational exponent in the equivalent expression to \root(3)(5)?Enter your response in fraction form
5^
5^
Answers
GPT-4o mini
The expression \(\sqrt[3]{5}\) can be rewritten using rational exponents. According to the rules of exponents, the nth root of a number can be expressed as that number raised to the power of \(\frac{1}{n}\).
In this case, since we are taking the cube root (3rd root) of 5, we can express it as:
\[
\sqrt[3]{5} = 5^{\frac{1}{3}}
\]
Thus, the rational exponent in the equivalent expression is \(\frac{1}{3}\).
In this case, since we are taking the cube root (3rd root) of 5, we can express it as:
\[
\sqrt[3]{5} = 5^{\frac{1}{3}}
\]
Thus, the rational exponent in the equivalent expression is \(\frac{1}{3}\).