Question

Which of the following is an equivalent expression to 7/ (−5.3)0 4⋅9 when applying the zero power rule?
7/1 + 4⋅9
7/5.3 + 4⋅9
7/0 + 4⋅9
7/5.3 with a power of 0 + 36

Answer 1

To solve the problem, we need to apply the zero power rule, which states that any non-zero number raised to the power of zero is equal to 1.

Looking at the expression:

\[
7 / (-5.3)^0 \cdot 4 \cdot 9
\]

We apply the zero power rule to \((-5.3)^0\):

\[
(-5.3)^0 = 1
\]

Thus, we can replace \((-5.3)^0\) with 1 in our expression:

\[
7 / 1 \cdot 4 \cdot 9
\]

Now we simplify this:

\[
7 / 1 = 7
\]

Next, we recognize that multiplying by \(4 \cdot 9\) means we will compute that product:

\[
4 \cdot 9 = 36
\]

So now we are left with:

\[
7 + 36
\]

This can be represented as:

\[
7 + 36
\]

Let's evaluate the answer options based on this conclusion:

1. **7 / 1 + 4⋅9** → This simplifies to \(7 + 36\).
2. **7 / 5.3 + 4⋅9** → Incorrect because we are not dividing by \(5.3\).
3. **7 / 0 + 4⋅9** → Incorrect as dividing by zero is undefined.
4. **7 / 5.3 with a power of 0 + 36** → Incorrect because 5.3 is not related to the zero power.

The correct equivalent expression is:

**7 / 1 + 4⋅9**.