Question

question 1 of 5
select the correct answer.
rewrite the following radical expression in rational exponent form.
$\left(\sqrt7{x}\
ight)^3$
$\left(\frac{1}{x^3}\
ight)^7$
$x^{\frac{7}{3}}$
$\frac{x^3}{x^7}$
$x^{\frac{3}{7}}$

Explanation:

Step1: Recall radical-exponent rule

For $\sqrt[n]{x}$, it equals $x^{\frac{1}{n}}$. So $\sqrt[7]{x} = x^{\frac{1}{7}}$.

Step2: Apply exponent power rule

When raising a power to a power, multiply exponents: $(x^a)^b = x^{a \cdot b}$. Here, $(x^{\frac{1}{7}})^3 = x^{\frac{1}{7} \times 3} = x^{\frac{3}{7}}$.

Answer:

D. $x^{\frac{3}{7}}$