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

Rewrite using a rational exponent. Assume all variables are positive.3√a5x10-example-1
User Haldagan
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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)}

User FarukT
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