Question

Reduce the following fraction: -36x^4y^4z^5/-12x^6y^3z

Answer 1

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------$

$\bf \cfrac{-36x^4y^4z^5}{-12x^6y^3z}\quad \begin{cases} 36=2\cdot 2\cdot 3\cdot 3\\ 12=2\cdot 2\cdot 3 \end{cases}\implies \cfrac{-36}{-12}\cdot \cfrac{x^4y^4z^5}{x^6y^3z^1} \\\\\\ \cfrac{\underline{-2\cdot 2\cdot 3}\cdot 3}{\underline{-2\cdot 2\cdot 3}}\cdot \cfrac{x^4y^4z^5x^{-6}y^{-3}z^{-1}}{1}\implies \cfrac{3}{1}\cdot \cfrac{x^4x^{-6}y^4y^{-3}z^5z^{-1}}{1}$

$\bf \cfrac{3}{1}\cdot \cfrac{x^{4-6}y^{4-3}z^{5-1}}{1}\implies \cfrac{3}{1}\cdot\cfrac{x^{-2}y^{1}z^4}{1}\implies \cfrac{3x^{-2}yz^4}{1}\implies \cfrac{3yz^4}{x^2}$