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Evaluate. (-1(1)/(4))^(2)=

Evaluate.\newline(−114)2= \left(-1 \frac{1}{4}\right)^{2}=

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Full solution

Q. Evaluate.\newline(−114)2= \left(-1 \frac{1}{4}\right)^{2}=
  1. Understand the problem: Understand the problem.\newlineWe need to find the square of the fraction −14-\frac{1}{4}, which means multiplying the fraction by itself.
  2. Convert to improper fraction: Convert the mixed number to an improper fraction.\newline−114-1\frac{1}{4} can be written as −54-\frac{5}{4} because −114=−1−14=−44−14=−54-1\frac{1}{4} = -1 - \frac{1}{4} = -\frac{4}{4} - \frac{1}{4} = -\frac{5}{4}.
  3. Square the fraction: Square the improper fraction.\newline(−54)2(-\frac{5}{4})^{2} means (−54)×(−54)(-\frac{5}{4}) \times (-\frac{5}{4}).
  4. Multiply numerators and denominators: Multiply the numerators and the denominators separately.(−5)×(−5)=25(-5) \times (-5) = 25 and 4×4=164 \times 4 = 16.
  5. Write down the result: Write down the result of the squaring. 2516\frac{25}{16} is the result of (−54)2(-\frac{5}{4})^{2}.

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