what is the simplest form of $sqrt3{x^{10}}$?\n$3sqrt3{x}$\n$xsqrt3{x}$\n$x^{3}sqrt3{x}$\n$3xsqrt3{x}$

Explanation:

Step1: Rewrite the exponent

We know that $x^{10}=x^{9 + 1}=(x^{3})^3\times x$. So, $\sqrt[3]{x^{10}}=\sqrt[3]{(x^{3})^3\times x}$.

Step2: Apply the cube - root property

According to the property $\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}$ ($a=(x^{3})^3$, $b = x$), we have $\sqrt[3]{(x^{3})^3\times x}=\sqrt[3]{(x^{3})^3}\times\sqrt[3]{x}$.

Step3: Simplify the cube - root

Since $\sqrt[3]{(x^{3})^3}=x^{3}$, then $\sqrt[3]{(x^{3})^3}\times\sqrt[3]{x}=x^{3}\sqrt[3]{x}$.

Answer:

$x^{3}\sqrt[3]{x}$