To find the value of \( (54)^{-3} \), we can rewrite it as:
\[ (54)^{-3} = \frac{1}{(54)^3} \]
Now we can calculate \( 54^3 \):
\[ 54^3 = 54 \times 54 \times 54 = 2916 \times 54 \]
Calculating \( 2916 \times 54 \):
\[ 2916 \times 54 = 157464 \]
Thus,
\[ (54)^{-3} = \frac{1}{157464} \]
Next, we’ll simplify:
Since the problem asked for the value in terms of fractions given in the responses, we can convert:
\[ (54)^{-3} = \frac{1}{(54)^3} = \frac{1}{(2 \cdot 27)^3} = \frac{1}{(2^3)(27^3)} = \frac{1}{8 \cdot 19683} = \frac{1}{157464} \]
Now let's match it with the given options.
To clarify, all the options provided seem to relate to negative exponents, which possibly could be about the inverse of bases of \( 125 \) and \( 64 \) as \( (5^3) \) and \( (4^3) \) respectively.
As you can see, \( 54^{-3} \) evaluates to a small value rather than what they provided, so potentially none of the proposed options might precisely connect to this.
On further investigation, it seems like your options might be indicating \( (4)^{-3} = \frac{1}{(4^3)} = \frac{1}{64} \) and \( (5)^{-3} = \frac{1}{(5^3)} = \frac{1}{125} \).
However, without more context or clarity on the specified base for \( (54)^{-3} \) since \( 125 \) or \( 64 \) are not directly used or any indication thereof, it may be an irrelevant choice unless specifically framed towards potential further clarification or matching elsewhere.
If taking a reverse of 54's components into 64 and 125, then \( 64 \) over \( 125 \) with a negation however led to looking different:
If further values matter, kindly clarify and I will assist on a path of clarity!