Which of the following is the equivalent expression to (15^−3 ⋅ 4^7)^0/4^−3

Question

that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses

164
Start Fraction 1 over 64 end fraction

1⋅4−3
1 times 4 negative cubed

604−3
Start Fraction 60 over 4 negative cubed end fraction

64
64
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Answer 1

To simplify the expression \((15^{-3} \cdot 4^7)^0 / 4^{-3}\), we can apply the properties of exponents.

1. First, recall that any non-zero number raised to the power of \(0\) is \(1\). Therefore: \[ (15^{-3} \cdot 4^7)^0 = 1 \]

2. Next, our expression simplifies to: \[ \frac{1}{4^{-3}} \]

3. We know that \(4^{-3} = \frac{1}{4^3}\) or inversely \(4^{-3} = \frac{1}{64}\). Thus: \[ \frac{1}{4^{-3}} = 4^3 = 64 \]

Therefore, the equivalent expression to \((15^{-3} \cdot 4^7)^0 / 4^{-3}\) using the properties of exponents is: \[ \boxed{64} \]