Question

rewrite the expression (sqrt6{729}) using a fractional exponent.(sqrt6{729} = 729^{square})(simplify your answer.)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to a fractional exponent is $\sqrt[n]{a}=a^{\frac{1}{n}}$, where $n$ is the index of the radical and $a$ is the radicand.

Step2: Apply the rule to the given expression

In the expression $\sqrt[6]{729}$, the index $n = 6$ and the radicand $a=729$. Using the rule $\sqrt[n]{a}=a^{\frac{1}{n}}$, we substitute $n = 6$ and $a = 729$. So $\sqrt[6]{729}=729^{\frac{1}{6}}$.

Answer:

$\frac{1}{6}$