Question

How do you work out: 4√c^12

Answer 1

$\bf 4\sqrt{c^{12}}~~ \begin{cases} c^{12}=c^{6\cdot 2}\\ \qquad (c^6)^2 \end{cases}\implies 4\sqrt{(c^6)^2}\implies 4c^6$

Answer 2

Consider the expression $4\sqrt{c^{12}}.$

First way:

You can write that $c^{12}=(c^6)^2.$ Then

$\sqrt{c^{12}}=\sqrt{(c^6)^2}=c^6$

and

$4\sqrt{c^{12}}=4c^6.$

Second way:

$4\sqrt{c^{12}}=4(c^{12})^{\frac{1}{2}}=4c^{\frac{12}{2}}=4c^6.$

Answer: $4\sqrt{c^{12}}=4c^6.$