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√((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)}=√((c^6)^2)=c^6`

and

`4\sqrt{c^(12)}=4c^6.`

Second way:

`4\sqrt{c^(12)}=4(c^(12))^{(1)/(2)}=4c^{(12)/(2)}=4c^6.`

Answer:
`4\sqrt{c^(12)}=4c^6.`