+2441 C; \(\sqrt[3]{x}\)
Why? Well, here we go. Let's start with the original:
\(\frac{\sqrt[3]{x^2}}{\sqrt[6]{x^2}}\) Change both of these square roots to exponents
\(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{6}}}\)
Now let's apply an exponent rule. The rule is the following.
\(\frac{x^a}{x^b}=x^{a-b}\)
Using this rule, we can simplify further:
\(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{6}}}=x^{\frac{2}{3}-\frac{1}{3}}\) I simplified 2/6 to 1/3. Now, subtract the exponents.
\(x^{\frac{1}{3}}=\sqrt[3]{x}\)This is your final answer. Hopefully, this makes sense...
