Question

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

A. -3x^2yz^4
B. 3yz^4/1x^2
C. -9yz^5/-3x^2
D. 36yz^5/12x^2

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}`