Which of the following is an equivalent expression to 7 over (−5.3)^0 + 4 ⋅ 9 when applying the Zero Power Rule?

Question

7 over 5.3 + 4 ⋅ 9

7 over 0 + 4 ⋅ 9

7 over 5.3^0 + 36

7 over 1 + 4 ⋅ 9

Answer 1

To determine the equivalent expression to $\frac{7}{(-5.3{)}^0}+4\cdot 9$ when applying the Zero Power Rule, we need to remember that any non-zero number raised to the power of 0 equals 1.

Thus,

$$(-5.3{)}^0=1$$

Substituting back into the expression, we have:

$$\frac{7}{1}+4\cdot 9$$

This simplifies to:

$$7+4\cdot 9$$

Now, calculating $4\cdot 9$:

$$4\cdot 9=36$$

So the expression now reads:

$$7+36$$

Now, let’s examine the answer choices:

1. $\frac{7}{5.3}+4\cdot 9$ — incorrect since $(-5.3{)}^0$ is not $5.3$.
2. $\frac{7}{0}+4\cdot 9$ — incorrect because $(-5.3{)}^0=1$, not 0.
3. $\frac{7}{{5.3}^0}+36$ — incorrect because ${5.3}^0$ should also equal 1 but does not match our derived expression.
4. $\frac{7}{1}+4\cdot 9$ — which is $7+36$ — correct.

Thus, the correct equivalent expression is:

$\frac{7}{1}+4\cdot 9$.