To evaluate \( 4^{-5} \), we can use the property of exponents that states \( a^{-b} = \frac{1}{a^b} \).
Thus, we have:
\[ 4^{-5} = \frac{1}{4^5} \]
Now, we need to calculate \( 4^5 \):
\[ 4^5 = 1024 \]
This means:
\[ 4^{-5} = \frac{1}{1024} \]
Now let's analyze the options given:
- \( -1024 \) - not equivalent
- \( 1024 \) - not equivalent
- \( 4^{-5} \) - equivalent as this is exactly what we have calculated
- "Two of these" - we have only found one equivalent.
Therefore, the correct answer is \( 4^{-5} \) which can be expressed as \( \frac{1}{1024} \). However, none of the two given option selections are appropriate.
On correction:
- None of the options are equivalent to \( 4^{-5} \).
- Only \( 4^{-5} \) directly refers to its own value and so is equivalent.
However, if the option provided \( \frac{1}{1024} \) were there, then that would stand.
But given your choices:
- None stands out (not covered directly).
So technically, saying two are equivalent could be misleading. The stated value in its respective expressions has to be closely matched. Hence, just focus on the calculation and interpret meanings of listed elements carefully.