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:

\( \frac{7}{1} + 4 \cdot 9 \).