To solve for \( 27^{43} \), we can express it in terms of the cube root:
Since \( 27 = 3^3 \), we can write:
\[ 27^{43} = (3^3)^{43} = 3^{3 \times 43} = 3^{129} \]
However, the options you've provided (81, 4, 12, 108) do not require computing \( 27^{43} \) in that manner. Instead, they seem to ask for a straightforward operation based on smaller powers or multiples.
- 81 is \( 3^4 \).
- 4 is \( 2^2 \).
- 12 is \( 3 \times 4 \).
- 108 is \( 3^3 \times 4 \).
There seems to be a misunderstanding with the numbers provided. If we need to choose a response based on powers of 3 or known results related to cube roots, none of the choices are correspondingly related to \( 27^{43} \).
Please clarify the problem or check if there has been an error in the options provided, as \( 27^{43} \) itself is not amongst them.
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