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:
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\( \frac{7}{0} + 4 \cdot 9 \) - This does not apply as \( \frac{7}{0} \) is undefined.
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\( \frac{7}{5.3^0} + 36 \) - This is equivalent to \( 7 + 36 \) since \( 5.3^0 = 1 \) and thus it simplifies correctly to \( 7 + 36 \).
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\( \frac{7}{5.3} + 4 \cdot 9 \) - 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:
\( \frac{7}{5.3^0} + 36 \)
3 answers