Converting a radical to a fractional exponent I want to understand how to convert a radical to a fractional exponent. Given the following equation:
$\sqrt[3]{(x)^6\cdot x^9}=\sqrt[3]{x^{24}\cdot x^9}=\sqrt[3]{x^{33}}=x^{\frac{33}3}=x^{11}$
How does: $\sqrt[3]{(x)^6\cdot x^9} = \sqrt[3]{x^{24}\cdot x^9}\;\;$??

Power rules of exponent :

*

*$(a^m)^n=a^{mn}$ $\to \sqrt[3]{(x^4)^6\cdot x^9} = \sqrt[3]{x^{24}\cdot x^9}$

*$a^ma^n=a^{m+n}$ $\to \sqrt[3]{x^{24}\cdot x^9}$$=\sqrt[3]{x^{33}}$

*$\sqrt[n]{a}=a^{\frac{1}{n}},\sqrt[n]{a^m}=a^{\frac{m}{n}}  \to  \sqrt[3]{x^{33}}$$=x^{\frac{33}{3}}=x^{11}\;$
Or,
$\sqrt[3]{(x^4)^6\cdot x^9} = \sqrt[3]{x^{24}\cdot x^9}$(2)$=\sqrt[3]{x^{33}}$$=x^{\frac{33}{3}}=x^{11}\;$
