Question

Show that:

$\frac{{\left(0.6\right)}^0-{\left(0.1\right)}^{-1}}{{\left(\frac{3}{8}\right)}^{-1}{\left(\frac{3}{2}\right)}^3+{\left(-\frac{1}{3}\right)}^{-1}}=-\frac{3}{2}$

Answer 1

$\frac{{\left(0.6\right)}^0-{\left(0.1\right)}^{-1}}{{\left(\frac{3}{8}\right)}^{-1}{\left(\frac{3}{2}\right)}^3+{\left(-\frac{1}{3}\right)}^{-1}}=-\frac{3}{2}$
zero power of any number is equal to $1$
$\frac{\frac{1}{1}-{\left(\frac{1}{10}\right)}^{-1}}{{\left(\frac{8}{3}\right)}^1{\left(\frac{3}{2}\right)}^3+{\left(-\frac{1}{3}\right)}^{-1}}$
$\frac{\frac{1}{1}-\frac{10}{1}}{\frac{8}{3}\times \frac{3\times 3\times 3}{2\times 2\times 2}+{\left(-3\right)}^1}$
$\frac{1-10}{9-3}$
$-\frac{3}{2}$