Given:
[tex]3^{-4}[/tex]
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.
[tex]\begin{gathered} 3^{-4}\text{ can also be written as (}\frac{1}{3})^4 \\ \end{gathered}[/tex]
The exponent 4 signifies that 1/3 will be multiplied by itself 4 times.
We will have:
[tex](\frac{1}{3})^4=\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}[/tex]
After that, we will multiply all the numerators and all the denominators.
[tex]\begin{gathered} (\frac{1}{3})^4=\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3}\cdot\frac{1}{3} \\ (\frac{1}{3})^4=\frac{1\cdot1\cdot1\cdot1}{3\cdot3\cdot3\cdot3} \\ (\frac{1}{3})^4=\frac{1}{81} \end{gathered}[/tex]
ANSWER: 1/81
