Question

Simplify this expression. (3c^5)^-6

Answer 1

We need to simplify the expression,

$(3c^5)^{-6}$

We are going to use the following exponent rule,

$\begin{gathered} (a^xb^y)^z \\ =a^{xz}b^{yz} \end{gathered}$

Let's simplify the expression with the rule shown above,

$\begin{gathered} (3c^5)^{-6} \\ =3^{-6}(c^5)^{-6} \\ =3^{-6}c^{-30} \end{gathered}$

We like to keep all exponents positive so we will use the following rule,

$a^{-x}=\frac{1}{a^x}$

So, the simplified form becomes:

$\begin{gathered} \frac{1}{3^6}\cdot\frac{1}{c^{30}} \\ =\frac{1}{729c^{30}} \end{gathered}$Answer$\frac{1}{729c^{30}}$