[tex]\bf 4\sqrt{c^{12}}~~ \begin{cases} c^{12}=c^{6\cdot 2}\\ \qquad (c^6)^2 \end{cases}\implies 4\sqrt{(c^6)^2}\implies 4c^6[/tex]
Consider the expression [tex]4\sqrt{c^{12}}.[/tex]
First way:
You can write that [tex]c^{12}=(c^6)^2.[/tex] Then
[tex]\sqrt{c^{12}}=\sqrt{(c^6)^2}=c^6[/tex]
and
[tex]4\sqrt{c^{12}}=4c^6.[/tex]
Second way:
[tex]4\sqrt{c^{12}}=4(c^{12})^{\frac{1}{2}}=4c^{\frac{12}{2}}=4c^6.[/tex]
Answer: [tex]4\sqrt{c^{12}}=4c^6.[/tex]
