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

60/4^−3
Start Fraction 60 over 4 negative cubed end fraction

64
64

1/64

Answer 1

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

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

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

3. Convert \(4^{-3}\): The negative exponent means we take the reciprocal: \[ 4^{-3} = \frac{1}{4^{3}}. \]

   Therefore, \[ \frac{1}{4^{-3}} = 4^{3}. \]

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

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

The correct answer from your options is: 64.