Question

Simplify the following :
${\left(\frac{1}{4}\right)}^{-2}-3\left(8{)}^{2/3}\right(4{)}^0+{\left(\frac{9}{16}\right)}^{\frac{-1}{2}}$

Answer 1

${\left(\frac{1}{4}\right)}^{-2}-3{\left(8\right)}^{\frac{2}{3}}(4{)}^0+{\left(\frac{9}{16}\right)}^{\frac{-1}{2}}$

$={\left({\left(\frac{1}{2}\right)}^2\right)}^{-2}-3{\left(2^3\right)}^{\frac{2}{3}}\left(1\right)+{\left(\frac{3^2}{4^2}\right)}^{\frac{-1}{2}}$

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

$={\left(\frac{1}{2}\right)}^{-4}-3{\left(2\right)}^2+{\left(\frac{3}{4}\right)}^{-1}$

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

$=16-12+\frac{4}{3}$

$=4+\frac{4}{3}$

$=\frac{16}{3}$