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

Question

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.