Which of the following is equivalent to 6^-2

Question

1/2^6
1/6^-2
1/36
36

Answer 1

To simplify $6^{-2}$, we can use the property that $a^{-n}=\frac{1}{a^n}$. Therefore:

$$6^{-2}=\frac{1}{6^2}$$

Calculating $6^2$:

$$6^2=36$$

Thus, we have:

$$6^{-2}=\frac{1}{36}$$

Now, let's evaluate the options given:

1. $\frac{1}{2^6}$
2. $\frac{1}{6^{-2}}$ (which is actually $6^2$)
3. $\frac{1}{36}$ (This matches our result)
4. $36$

The only expression that is equivalent to $6^{-2}$ is:

$$\frac{1}{36}$$

So the correct answer is $\frac{1}{36}$.