Question

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 1⋅4−3 1 times 4 negative cubed 164 Start Fraction 1 over 64 end fraction 64 64 604−3

Answer 1

To simplify the expression \((15 - 3 \cdot 47) \cdot 4^{-3}\), we first calculate \(15 - 3 \cdot 47\):

1. Calculate \(3 \cdot 47 = 141\).
2. Then, \(15 - 141 = -126\).
3. Now we substitute this back into the expression:
\[
-126 \cdot 4^{-3}
\]

Next, we can rewrite \(4^{-3}\) as \(\frac{1}{4^3}\):
\[
-126 \cdot \frac{1}{4^3} = \frac{-126}{4^3}
\]

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

Substituting that in gives:
\[
\frac{-126}{64}
\]

This can be simplified:
Since both -126 and 64 can be divided by 2:

\[
\frac{-63}{32}
\]

However, I assumed we're looking for equivalent expressions. None of the answers seem to directly match our calculation \(\frac{-63}{32}\), so let's see if we can match any of the available responses:
1. \(1 \cdot 4^{-3} = 4^{-3}\)
2. \(164 = \frac{1}{64}\)
3. \(64\)
4. \(60 \cdot 4^{-3}\)

Among them, we find that \(4^{-3} = \frac{1}{64}\).

Thus, from your options, it looks like the equivalent expression is:
\[
\frac{1}{64}
\]

So the correct response to select is:
**\(\frac{1}{64}\)**.