Given:
The expression is given as,
[tex]\sqrt[]{36p^{10}m^6}[/tex]
The objective is to rewrite the expression without any radical form.
Explanation:
The given expression can be written as,
[tex]\sqrt[]{36p^{10}m^6}=\sqrt[]{6^2p^{10}m^6}\text{ . . . . .(1)}[/tex]
In general, the radical form of a square root can be written as,
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]
Then, the equation (1) can be written as
[tex]\sqrt[]{36p^{10}m^6}=(6^2p^{10}m^6)^{\frac{1}{2}}[/tex]
On further solving the above expression,
[tex]\begin{gathered} \sqrt[]{36p^{10}m^6}=6^{2\times\frac{1}{2}}p^{10\times\frac{1}{2}}m^{6\times\frac{1}{2}} \\ =6p^5m^3 \end{gathered}[/tex]
Hence, the simplified expression of the given term is,
[tex]6p^5m^3[/tex]
