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)=(1)/(a^x)`

So, the simplified form becomes:

`\begin{gathered} (1)/(3^6)\cdot(1)/(c^(30)) \\ =(1)/(729c^(30)) \end{gathered}`Answer
`(1)/(729c^(30))`