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

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

64
64

164
Start Fraction 1 over 64 end fraction

1⋅4−3

Answer 1

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

1. First, we note that any expression raised to the power of 0 equals 1: \[ (15^{-3} \cdot 4^7)^0 = 1 \]

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

3. Applying the property of negative exponents, \(a^{-n} = \frac{1}{a^n}\), we find: \[ 4^{-3} = \frac{1}{4^3} \] Thus, \[ 1 / 4^{-3} = 1 \cdot 4^{3} = 4^3 \]

4. Now, we calculate \(4^3\): \[ 4^3 = 64 \]

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

The answer is: 64