Question

Hi tried this question on my own and I got 1/12 which was not right so I’m not sure what I did wrong

Answer 1

Given:

`3^(-4)`

Asked: Rewrite without an exponent.

Solution:

To solve this problem, we will be dealing with the negative exponent. Because the exponent is negative, we will reverse 3 and it will become 1/3 then raise it to positive 4.

`\begin{gathered} 3^(-4)\text{ can also be written as (}(1)/(3))^4 \\ \end{gathered}`

The exponent 4 signifies that 1/3 will be multiplied by itself 4 times.

We will have:

`((1)/(3))^4=(1)/(3)\cdot(1)/(3)\cdot(1)/(3)\cdot(1)/(3)`

After that, we will multiply all the numerators and all the denominators.

`\begin{gathered} ((1)/(3))^4=(1)/(3)\cdot(1)/(3)\cdot(1)/(3)\cdot(1)/(3) \\ ((1)/(3))^4=(1\cdot1\cdot1\cdot1)/(3\cdot3\cdot3\cdot3) \\ ((1)/(3))^4=(1)/(81) \end{gathered}`

ANSWER: 1/81