Answer
$7(c^{1})^{8}=7c^{8}$
Work Step by Step
$7(c^{1})^{?}=7c^{8}$
Since $7$ is a factor on both sides of the equation, it plays no role in the equation. If we were solving it, we would divide by $7$ and it would cancel on both sides.
To raise a power to a power, we multiply the exponents. Therefore, in order for this equation to be correct, the product of $1$ and the second exponent must equal $8$. The only way this would work is if the second exponent is $8$, because $1\times8=8$.
Therefore the correct equation is $7(c^{1})^{8}=7c^{8}$
