Question
Which of the following is equivalent to 3−4 ? Show your work. (1 point) Responses 81 81 181 1 over 81 13−4 the fraction with numerator 1 and denominator 3 to the negative 4 power −81
Answers
GPT-4o mini
To simplify \(3^{-4}\), we can use the rule of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\).
So, we can rewrite \(3^{-4}\) as:
\[
3^{-4} = \frac{1}{3^4}
\]
Next, we calculate \(3^4\):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Now, substituting back into our expression:
\[
3^{-4} = \frac{1}{81}
\]
Therefore, the equivalent expression for \(3^{-4}\) is:
\[
\frac{1}{81}
\]
From the provided responses, the correct answer is \( \frac{1}{81} \).
So, we can rewrite \(3^{-4}\) as:
\[
3^{-4} = \frac{1}{3^4}
\]
Next, we calculate \(3^4\):
\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]
Now, substituting back into our expression:
\[
3^{-4} = \frac{1}{81}
\]
Therefore, the equivalent expression for \(3^{-4}\) is:
\[
\frac{1}{81}
\]
From the provided responses, the correct answer is \( \frac{1}{81} \).