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marishachu [46]
3 years ago
6

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

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0
\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}
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