To simplify the expression \((15^{-3} \cdot 4^{7})^{0}/4^{-3}\), we can apply the properties of exponents step by step.
- Applying the Zero Exponent Property: Any non-zero base raised to the power of 0 equals 1, so:
\[ (15^{-3} \cdot 4^{7})^{0} = 1 \]
- Substituting back into the expression: Now we can substitute this into the original expression:
\[ \frac{1}{4^{-3}} \]
- Applying the Negative Exponent Rule: The negative exponent property states that \(a^{-n} = \frac{1}{a^{n}}\). Therefore:
\[ \frac{1}{4^{-3}} = 4^{3} \]
- Calculating \(4^{3}\): Now we can calculate \(4^{3}\):
\[ 4^{3} = 64 \]
So the equivalent expression for \((15^{-3} \cdot 4^{7})^{0}/4^{-3}\) is:
\[ \boxed{64} \]