Question
Which of the following is equivalent to 3^−4
?
Show your work.
(1 point)
Responses
18/1
1 over 81
−81
negative 81
81
81
1/3^−4
?
Show your work.
(1 point)
Responses
18/1
1 over 81
−81
negative 81
81
81
1/3^−4
Answers
GPT-4o mini
To find the equivalent value of \( 3^{-4} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).
So,
\[
3^{-4} = \frac{1}{3^{4}}.
\]
Now, we can calculate \( 3^{4} \):
\[
3^{4} = 3 \times 3 \times 3 \times 3 = 9 \times 9 = 81.
\]
Therefore,
\[
3^{-4} = \frac{1}{3^{4}} = \frac{1}{81}.
\]
Looking at the provided options, the equivalent to \( 3^{-4} \) is:
\[
\text{1 over 81}.
\]
So,
\[
3^{-4} = \frac{1}{3^{4}}.
\]
Now, we can calculate \( 3^{4} \):
\[
3^{4} = 3 \times 3 \times 3 \times 3 = 9 \times 9 = 81.
\]
Therefore,
\[
3^{-4} = \frac{1}{3^{4}} = \frac{1}{81}.
\]
Looking at the provided options, the equivalent to \( 3^{-4} \) is:
\[
\text{1 over 81}.
\]