To create an equivalent expression for "five sevenths raised to the negative first power times eighteen hundredths raised to the second power," we can break it down as follows:
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Five sevenths raised to the negative first power is the same as the reciprocal of five sevenths. Therefore: \[ \left(\frac{5}{7}\right)^{-1} = \frac{7}{5} \]
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Eighteen hundredths raised to the second power can be represented as: \[ (0.18)^2 \]
Putting this together, the expression "five sevenths raised to the negative first power times eighteen hundredths raised to the second power" can be written as: \[ \frac{7}{5} \times (0.18)^2 \]
Now let's analyze the answer choices:
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\((1.4)(0.18)^2\): Not equivalent since \( \frac{7}{5} \) equals 1.4, but the expression is not structured like the original.
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\((0.714)(0.18)^2\): Not equivalent since \( \frac{7}{5} \) is not equal to 0.714.
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Seven fifths raised to the first power times the quantity one over eighteen hundredths raised to the second power:
- This option can be represented as: \[ \frac{7}{5} \times \left(\frac{1}{0.18}\right)^2 \] This is not equivalent to the original expression.
Thus, the most straightforward equivalent expression based on the breakdown, as noted in point 2, would be:
\(\frac{7}{5} \times (0.18)^2\)
However, among the provided options, none are fully correct. The correct answer, in terms of structure, is represented as \(\frac{7}{5}(0.18)^2\) based on our breakdown.
If we must select one based only on the transformations done, the choice matching the structure would be: seven fifths raised to the first power times the quantity one over eighteen hundredths raised to the second power as it at least acknowledges the fraction involved with the actual operation described.
1 answer