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

User JimmyJ
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1 Answer

6 votes

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))

User Beeb
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7.1k points