Question

Which of the following is equivalent to 3^-4?
-81
1/81
81
1/3^-4

Answer 1

To find the equivalent value of \( 3^{-4} \), we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

So,

\[
3^{-4} = \frac{1}{3^4}
\]

Now, we calculate \( 3^4 \):

\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\]

Therefore,

\[
3^{-4} = \frac{1}{3^4} = \frac{1}{81}
\]

Now looking at the options:

- 81
- \( \frac{1}{81} \)
- 1
- \( \frac{1}{3^{-4}} \)

The equivalent value to \( 3^{-4} \) is \( \frac{1}{81} \).

Thus, the correct answer is:

\(\frac{1}{81}\)