Which exponential expression is equal to \( \frac{4^{3}}{4^{-2}} \) ? A \( \frac{4^{-3}}{4^{-2}} \) B \( \frac{4^{3}}{4^{2}} \) C \( \left(4^{-1}\right)^{-5} \) D \( \left(4^{4}\right)^{1} \)

To solve the expression \( \frac{4^{3}}{4^{-2}} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Therefore, we can rewrite the expression as \( 4^{3 - (-2)} = 4^{3 + 2} = 4^{5} \). Now, let's analyze the options one by one: A: \( \frac{4^{-3}}{4^{-2}} = 4^{-3 - (-2)} = 4^{-3 + 2} = 4^{-1} \) (not equal to \( 4^{5} \)) B: \( \frac{4^{3}}{4^{2}} = 4^{3 - 2} = 4^{1} \) (not equal to \( 4^{5} \)) C: \( \left(4^{-1}\right)^{-5} = 4^{-1 \cdot -5} = 4^{5} \) (this one is equal to \( 4^{5} \)) D: \( \left(4^{4}\right)^{1} = 4^{4} \) (not equal to \( 4^{5} \)) Thus, the correct exponential expression that is equal to \( \frac{4^{3}}{4^{-2}} \) is C: \( \left(4^{-1}\right)^{-5} \).