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

Question

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

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

164
Start Fraction 1 over 64 end fraction

1⋅4−3
1 times 4 negative cubed

64

Answer 1

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

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

2. Now we rewrite the entire expression: \[ \frac{1}{4^{-3}} \]

3. Using the property of negative exponents (\(a^{-n} = \frac{1}{a^{n}}\)): \[ \frac{1}{4^{-3}} = 4^{3} \]

4. Calculating \(4^{3}\): \[ 4^{3} = 64 \]

Thus, the equivalent expression is

\[ 64 \]

Therefore, the correct response is 64.