# What is (6^3 - 2^6)/(2^3) ?

Jul 20, 2016

$19$

#### Explanation:

The boring way would be to pick up a calculator and push buttons,,

Lets' explore a bit. Separate the fraction into two separate fractions each with its own denominator. At the same time write $6 = 2 \times 3$

${\left(2 \times 3\right)}^{3} / {2}^{3} - {2}^{6} / {2}^{3} \text{ (right side simplifies to} {2}^{3}$ )

=$\frac{{2}^{3} \times {3}^{3}}{2} ^ 3 - {2}^{3}$

=$\frac{{\cancel{2}}^{3} \times {3}^{3}}{\cancel{2}} ^ 3 - {2}^{3}$

=${3}^{3} - {2}^{3}$

=$27 - 8 = 19$