Question

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

71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9

75.30+36
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36

70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9

7/5.3+4⋅9

Answer 1

To apply the Zero Power Rule, we need to understand that any non-zero number raised to the power of zero equals 1. In this case, the expression is:

\[ 7(-5.3)^0 + 4 \cdot 9 \]

According to the Zero Power Rule:

\[ (-5.3)^0 = 1 \]

Therefore, the expression simplifies to:

\[ 7 \cdot 1 + 4 \cdot 9 \]

This simplifies further to:

\[ 7 + 36 \]

Thus, the equivalent expression is:

\[ 7 + 4 \cdot 9 = 7 + 36 \]

Now, let's look at the given options:

1. \( 71 + 4 \cdot 9 \)
2. \( \frac{7}{5.3^0} + 36 \)
3. \( 70 + 4 \cdot 9 \)
4. \( \frac{7}{5.3} + 4 \cdot 9 \)

The correct form is:

\( 71 + 4 \cdot 9 \)

Since \( 7 \) is just a misrepresentation of \( 7 + 0 \) which is not needed here.

So, the equivalent expression among the choices is **option 1: \( 7 + 4 \cdot 9 \)**.