Apply All Exponent Rules Quick Check

Question

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Question
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)
Responses

1/64
Start Fraction 1 over 64 end fraction

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

64
64

1⋅4^−3

Answer 1

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

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

2. So, the entire expression simplifies to: \[ \frac{1}{4^{-3}} \]

3. Recalling that \(\frac{1}{a^{-b}} = a^{b}\): \[ \frac{1}{4^{-3}} = 4^{3} = 64 \]

So, the equivalent expression is:

\[ \boxed{64} \]

Thus, the correct response is:

• 64