Which of the following is equivalent to 3^-4? Show your work.

Answer 1

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

Applying this property:

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

Now, we can calculate \( 3^{4} \):

\[ 3^{4} = 3 \times 3 \times 3 \times 3 \]

Calculating step by step:

1. \( 3 \times 3 = 9 \)
2. \( 9 \times 3 = 27 \)
3. \( 27 \times 3 = 81 \)

So, \( 3^{4} = 81 \).

Now we have:

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

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