Question

Rewrite using a rational exponent. Assume all variables are positive.3√a5x10

Answer 1

Note that a radical expression can be express in rational exponents :

$\sqrt[n]{a}=a^{\frac{1}{n}}$

From the problem, we have :

$\sqrt[3]{a^5x^{10}}=(a^5x^{10})^{\frac{\frac{1}{1}}{3}}$

When simplifying exponents with parenthesis, the exponents are multiplied with each other.

$(a^m)^n=a^{mn}^{}$

So we have :

$\begin{gathered} (a^5x^{10})^{\frac{1}{3}}=a^{5\times\frac{1}{3}}x^{10\times\frac{1}{3}} \\ \Rightarrow a^{\frac{5}{3}}x^{\frac{10}{3}} \end{gathered}$

The answer is :

$a^{\frac{5}{3}}x^{\frac{10}{3}}$