Question

Solve $({\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{2}\right)}^{-3})÷{\left(\frac{1}{4}\right)}^{-3}$

Answer 1

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

$\Rightarrow \left(\left(-\frac{1}{3}\times -\frac{1}{3}\times -\frac{1}{3}\right)-\left(-\frac{1}{2}\times -\frac{1}{2}\times -\frac{1}{2}\right)\right)÷\left(-\frac{1}{4}\times -\frac{1}{4}\times -\frac{1}{4}\right)$

$\Rightarrow \left(\left(-\frac{1}{27}\right)-\left(-\frac{1}{8}\right)\right)÷\left(-\frac{1}{64}\right)$

$\Rightarrow \left(-\frac{1}{27}+\frac{1}{8}\right)÷\left(-\frac{1}{64}\right)$

$\Rightarrow \frac{-8+27}{216}\times -64$

$\Rightarrow \frac{-19}{216}\times -64$

$\Rightarrow 5.629$

$\Rightarrow 5.63$