which expression is equivalent to $\frac{(6x^{5}z)^{3}}{4x^{4}z^{2}}$?\n$\frac{3x^{4}z^{2}}{2}$\n$54x^{11}z$\…

which expression is equivalent to $\frac{(6x^{5}z)^{3}}{4x^{4}z^{2}}$?\n$\frac{3x^{4}z^{2}}{2}$\n$54x^{11}z$\n$\frac{9x^{11}z}{2}$\n$54x^{19}z^{5}$

which expression is equivalent to $\frac{(6x^{5}z)^{3}}{4x^{4}z^{2}}$?\n$\frac{3x^{4}z^{2}}{2}$\n$54x^{11}z$\n$\frac{9x^{11}z}{2}$\n$54x^{19}z^{5}$

Answer

Explanation:

Step1: Expand el numerador

Usamos la regla $(ab)^n=a^n b^n$ y $(a^m)^n=a^{mn}$. $$(6x^{5}z)^{3}=6^{3}x^{5\times3}z^{3}=216x^{15}z^{3}$$

Step2: Simplificar la fracción

Tenemos $\frac{216x^{15}z^{3}}{4x^{4}z^{2}}$. Usamos la regla $\frac{a^m}{a^n}=a^{m - n}$ y $\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$. $$\frac{216}{4}\times\frac{x^{15}}{x^{4}}\times\frac{z^{3}}{z^{2}} = 54x^{15 - 4}z^{3 - 2}=54x^{11}z$$

Answer:

$54x^{11}z$ (segunda opción)