Question

Carry out the following division: $34{\mathrm{x}}^3{\mathrm{y}}^3{\mathrm{z}}^3÷51{\mathrm{xy}}^2{\mathrm{z}}^3$

Answer 1

Find: $34{\mathrm{x}}^3{\mathrm{y}}^3{\mathrm{z}}^3÷51{\mathrm{xy}}^2{\mathrm{z}}^3$

$\begin{array}{rcl}\frac{34{\mathrm{x}}^3{\mathrm{y}}^3{\mathrm{z}}^3}{51{\mathrm{xy}}^2{\mathrm{z}}^3}& =& \frac{34}{51}\times \frac{{\mathrm{x}}^3}{{\mathrm{x}}^1}\times \frac{{\mathrm{y}}^3}{{\mathrm{y}}^2}\times \frac{{\mathrm{z}}^3}{{\mathrm{z}}^3}\\ & =& \frac{2}{3}\times {\mathrm{x}}^{3-1}\times {\mathrm{y}}^{3-2}\times {\mathrm{z}}^{3-3}\\ & =& \frac{2}{3}\times {\mathrm{x}}^2\times {\mathrm{y}}^1\times {\mathrm{z}}^0\left[\mathrm{Note}:\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}},{\mathrm{a}}^0=1\right]\\ & =& \frac{2{\mathrm{x}}^2\mathrm{y}}{3}\end{array}$

Hence, $34{\mathrm{x}}^3{\mathrm{y}}^3{\mathrm{z}}^3÷51{\mathrm{xy}}^2{\mathrm{z}}^3=\frac{2{\mathrm{x}}^2\mathrm{y}}{3}$