Questions: -left(frac25right)^3 = frac2^2-5 =

-left(frac25right)^3 = frac2^2-5 =
Transcript text: \[ \begin{aligned} -\left(\frac{2}{5}\right)^{3} & = \\ \frac{2^{2}}{-5} & = \end{aligned} \]
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Solution

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Solution Steps

To solve the given mathematical expressions, we need to evaluate the power and fraction operations as specified.

  1. For the first expression, \(-\left(\frac{2}{5}\right)^{3}\), we need to cube the fraction \(\frac{2}{5}\) and then apply the negative sign.
  2. For the second expression, \(\frac{2^{2}}{-5}\), we need to square the numerator (2) and then divide by the denominator (-5).
Step 1: Evaluate \(-\left(\frac{2}{5}\right)^{3}\)

To evaluate \(-\left(\frac{2}{5}\right)^{3}\), we first cube the fraction \(\frac{2}{5}\): \[ \left(\frac{2}{5}\right)^{3} = \frac{2^3}{5^3} = \frac{8}{125} \] Then, we apply the negative sign: \[ -\left(\frac{8}{125}\right) = -0.0640 \]

Step 2: Evaluate \(\frac{2^{2}}{-5}\)

To evaluate \(\frac{2^{2}}{-5}\), we first square the numerator: \[ 2^{2} = 4 \] Then, we divide by the denominator: \[ \frac{4}{-5} = -0.8000 \]

Final Answer

\[ -\left(\frac{2}{5}\right)^{3} = \boxed{-0.0640} \] \[ \frac{2^{2}}{-5} = \boxed{-0.8000} \]

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