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 70+4⋅9 Start Fraction 7 over 0 End Fraction plus 4 times 9 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 75.3+4⋅9

Answer 1

The Zero Power Rule states that any non-zero number raised to the power of zero equals 1. Therefore, in the expression \( 7(-5.3)^0 + 4 \cdot 9 \), we can simplify \((-5.3)^0\) to \(1\).

So the expression simplifies as follows:

\[
7(-5.3)^0 + 4 \cdot 9 = 7 \cdot 1 + 4 \cdot 9 = 7 + 36
\]

Now let's look for equivalent expressions in the given responses:

- \( 70 + 4 \cdot 9 \) → No, since \(7 + 36\) becomes \(43\).
- \( \frac{7}{0} + 4 \cdot 9 \) → No, since this involves division by zero which is undefined.
- \( \frac{7}{1} + 4 \cdot 9 \) → No, because that simplifies to \(7 + 36\) which equals \(43\), but is not represented correctly in this option.
- \( 75.3 + 36 \) → No, since this does not match \(7 + 36\).
- \( 75.3 + 4 \cdot 9 \) → No.

None of the provided options are fully correct equivalents in terms of the outcome. The correct simplification of the original expression \( 7(-5.3)^0 + 4 \cdot 9 \) results in \( 43\) and does not match any of the listed options.

If corrected where \(75.3\) should instead be \(7\) (assuming a potential typo), then the expression would be equivalent to \(7 + 36\).

If none is adjusted for clarity, then the expressions do not provide acceptable equivalencies for the question posed. The completed evaluation is:

1. \( 43\) as correct value achieved, but not listed.
2. Verifying responses for logical accuracy or typographical errors which may create confusion.