Which of the following is the equivalent expression to (15^−3 ⋅ 4^7)^0/4^−3 that has been generated by applying the Properties of Integer Exponents?(1 point)

Question

Responses

1⋅4−3
1 times 4 negative cubed

164
Start Fraction 1 over 64 end fraction

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

64

Answer 1

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

1. Applying the zero exponent rule: Any non-zero number raised to the power of zero is 1. \[ (15^{-3} \cdot 4^{7})^{0} = 1 \]

2. Now substitute this back into the expression: \[ \frac{1}{4^{-3}} \]

3. Apply the negative exponent rule: \(4^{-3}\) can be rewritten as \( \frac{1}{4^3}\), thus: \[ \frac{1}{4^{-3}} = 4^{3} \]

4. Calculate \(4^3\): \[ 4^3 = 64 \]

So, the expression simplifies to \(64\).

Therefore, the equivalent expression is: \[ 64 \]

Thus, the correct answer is: 64.