Question

Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3
that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses

64
64

164
Start Fraction 1 over 64 end fraction

1⋅4−3
1 times 4 negative cubed

604−3

Answer 1

To simplify the expression \( (15 - 3 \cdot 47) \cdot 04^{-3} \), let's start by calculating each part:

1. First, evaluate \( 15 - 3 \cdot 47 \):
\[
3 \cdot 47 = 141
\]
Thus,
\[
15 - 141 = -126
\]

2. Now, consider the expression. The first part evaluates to \(-126\), but we also need to calculate \( 04^{-3} \):
\[
04^{-3} = 0^{-3}
\]
However, \( 0^{-3} \) is undefined, as division by zero is not allowed.

It looks like the correct interpretation should evaluate only the exponent part. The expression can actually be simplified to focus on the exponent:

If we rewrite \( 4^{-3} \):
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}
\]

However, without the non-zero multiplication from \( -126 \), if we only focus on \( 04^{-3} \), we end up with:
\[
0 \cdot \frac{1}{64} = 0
\]

But from the options you provided, the equivalent expression depends solely on the exponent:

- \( 64 \)
- \( \frac{1}{64} \)
- \( 1 \cdot 4^{-3} \)
- \( 60 \cdot 4^{-3} \)

Given the directly applicable properties of integer exponents, the best equivalent expression based solely on the exponent, excluding the zero factor, is:

**Option: \( \frac{1}{64} \)** (as it is equivalent to \( 4^{-3} \)).