Question

Simplify the following :

${\left(-\frac{2}{5}\right)}^3\times {\left(-\frac{1}{4}\right)}^2$

Answer 1

Step 1: Find the value of ${\left(-\frac{2}{5}\right)}^3$ and ${\left(-\frac{1}{4}\right)}^2$.

Given: ${\left(-\frac{2}{5}\right)}^3\times {\left(-\frac{1}{4}\right)}^2$

We know that

$(-1)$^{odd number} = negative answer

$(-1)$^{even number} = positive answer

$$\begin{gathered} {\left(-\frac{2}{5}\right)}^3=\left(-\frac{2}{5}\right)\times \left(-\frac{2}{5}\right)\times \left(-\frac{2}{5}\right) \\ =-\frac{2\times 2\times 2}{5\times 5\times 5} \\ =-\frac{8}{125} \end{gathered}$$

$$\begin{gathered} {\left(-\frac{1}{4}\right)}^2=\left(-\frac{1}{4}\right)\times \left(-\frac{1}{4}\right) \\ =\frac{1\times 1}{4\times 4} \\ =\frac{1}{16} \end{gathered}$$

Step 2: Find the value of ${\left(-\frac{2}{5}\right)}^3\times {\left(-\frac{1}{4}\right)}^2$

Now,

$$\begin{gathered} {\left(-\frac{2}{5}\right)}^3\times {\left(-\frac{1}{4}\right)}^2=-\frac{8}{125}\times \frac{1}{16} \\ =-\frac{{\cancel{8}}^1}{125}\times \frac{1}{{\cancel{16}}^2} \\ =-\frac{1\times 1}{125\times 2} \\ =-\frac{1}{250} \end{gathered}$$

Hence, ${\left(-\frac{2}{5}\right)}^3\times {\left(-\frac{1}{4}\right)}^2=-\frac{1}{250}$.