Question

Which of the following is an equivalent expression to 7/(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)

7/0+4⋅9

7/5.3^0+36

7/5.3+4⋅9

Answer 1

To evaluate the expression \( \frac{7}{(-5.3)^0} + 4 \cdot 9 \) using the Zero Power Rule, we first apply the rule itself, which states that any non-zero number raised to the power of zero is 1.

Since \( (-5.3)^0 = 1 \), we have:

\[
\frac{7}{(-5.3)^0} + 4 \cdot 9 = \frac{7}{1} + 4 \cdot 9
\]

This simplifies to:

\[
7 + 4 \cdot 9
\]

Now, let's simplify \( 4 \cdot 9 \):

\[
4 \cdot 9 = 36
\]

So the expression becomes:

\[
7 + 36
\]

None of the answer choices provided can be obtained directly from the original expression using the zero power rule. However, if we look closely at the options given:

1. \( \frac{7}{0} + 4 \cdot 9 \) - This does not apply as \( \frac{7}{0} \) is undefined.

2. \( \frac{7}{5.3^0} + 36 \) - This is equivalent to \( 7 + 36 \) since \( 5.3^0 = 1 \) and thus it simplifies correctly to \( 7 + 36 \).

3. \( \frac{7}{5.3} + 4 \cdot 9 \) - This is incorrect as \( 5.3^0 \neq 5.3 \) when applying the zero power rule.

The option that correctly represents an equivalent expression when applying the Zero Power Rule is:

**\( \frac{7}{5.3^0} + 36 \)**