Question

tenth root of the quantity x to the fifth times x to the fourth times x squared end quantity

Answer 1

Given:

$\sqrt[10]{x^5\times x^4\times x^2}$

To Determine: The simplification of the given

Solution

Given the exponent rule below

$a^m\times a^n=a^{m+n}$

Applying the rule to the given

$\sqrt[10]{x^5\times x^4\times x^2}=\sqrt[10]{x^{5+4+2}}=\sqrt[10]{x^{11}}$

Given the exponent rule below

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

Applying the exponent rule to the given

$\begin{gathered} \sqrt[10]{x^5x^4x^2}=\sqrt[10]{x^{11}}=x^{\frac{11}{10}} \\ Therefore \\ \sqrt[10]{x^5x^4x^2}=x^{\frac{11}{10}} \end{gathered}$

The answer is

$x^{\frac{11}{10}}$