Let's simplify the expression step-by-step, starting with \((15^{-3} \times 4^{7})^{0} / 4^{-3}\).
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Simplify the power of zero:
Anything raised to the power of zero is equal to 1, so: \[ (15^{-3} \times 4^{7})^{0} = 1 \] -
Substitute back into the equation: Now we substitute this back, giving us: \[ 1 / 4^{-3} \]
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Apply the property of exponents for negative exponents:
Recall that \(a^{-n} = \frac{1}{a^{n}}\), thus: \[ 1 / 4^{-3} = 1 \times 4^{3} = 4^{3} \] -
Evaluate \(4^{3}\): \[ 4^{3} = 64 \]
So, the equivalent expression is: \[ \boxed{64} \]