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^{(1)/(n)}`

From the problem, we have :

`\sqrt[3]{a^5x^(10)}=(a^5x^(10))^{((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))^{(1)/(3)}=a^{5*(1)/(3)}x^{10*(1)/(3)} \\ \Rightarrow a^{(5)/(3)}x^{(10)/(3)} \end{gathered}`

The answer is :

`a^{(5)/(3)}x^{(10)/(3)}`