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* x^4* x^2}`

To Determine: The simplification of the given

Solution

Given the exponent rule below

`a^m* a^n=a^(m+n)`

Applying the rule to the given

`\sqrt[10]{x^5* x^4* x^2}=\sqrt[10]{x^(5+4+2)}=\sqrt[10]{x^(11)}`

Given the exponent rule below

`\sqrt[m]{a^n}=a^{(n)/(m)}`

Applying the exponent rule to the given

`\begin{gathered} \sqrt[10]{x^5x^4x^2}=\sqrt[10]{x^(11)}=x^{(11)/(10)} \\ Therefore \\ \sqrt[10]{x^5x^4x^2}=x^{(11)/(10)} \end{gathered}`

The answer is

`x^{(11)/(10)}`