Question

Simplify :

${\left[{\left(-\frac{3}{4}\right)}^2\right]}^2$

Answer 1

Given; ${\left[{\left(-\frac{3}{4}\right)}^2\right]}^2$.

We know that

${\left[{\left(\mathrm{a}\right)}^{\mathrm{m}}\right]}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}$.

Now,

${\left[{\left(-\frac{3}{4}\right)}^2\right]}^2={\left(-\frac{3}{4}\right)}^{2\times 2}\left[\because {\left[{\left(\mathrm{a}\right)}^{\mathrm{m}}\right]}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}\right]$

$$\begin{gathered} ={\left(-\frac{3}{4}\right)}^4 \\ =\left(-\frac{3}{4}\right)\times \left(-\frac{3}{4}\right)\times \left(-\frac{3}{4}\right)\times \left(-\frac{3}{4}\right) \\ =\frac{81}{256} \end{gathered}$$

Hence, ${\left[{\left(-\frac{3}{4}\right)}^2\right]}^2=\frac{81}{256}$