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

$-left(frac25right)^3 = frac2^2-5 =$

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

Solution

Solution Steps

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

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.
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: \[ \frac{4}{-5} = -0.8000 \]