Question

Ayudenme con este deber 200 puntos a la mejor respuesta que tenga proceso y todo
El ejercicio 336 y 337

Answer 1

$\left(\frac{d^4}{a^{-3}b^{-2}c^{-1}}\left(\frac{b^2d^2}{a^2c^2}\right)^{-2}\left(c^2\left(\frac{1}{ab^2}\right)^{-3}\right)^4\frac{a^{-10}}{b^{10}d^{-1}}\right)^3$
Resolver por partes:
$\frac{d^4}{a^{-3}b^{-2}c^{-1}}$
$\mathrm{Multiplicar\:}a^{-3}b^{-2}c^{-1}\::$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^{-b}=\frac{1}{a^b}$
$a^{-3}=\frac{1}{a^3}$
$=b^{-2}c^{-1}\frac{1}{a^3}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^{-b}=\frac{1}{a^b}$
$b^{-2}=\frac{1}{b^2}$
$=c^{-1}\frac{1}{a^3}\cdot \frac{1}{b^2}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^{-1}=\frac{1}{a}$
$c^{-1}=\frac{1}{c}$
$=\frac{1}{c}\cdot \frac{1}{a^3}\cdot \frac{1}{b^2}$
$=\frac{1}{a^3b^2c}$
$=\frac{d^4}{\frac{1}{a^3b^2c}}$
$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$
$=\frac{d^4a^3b^2c}{1}$
$=d^4a^3b^2c$

$=\left(d^4a^3b^2c\frac{a^{-10}}{d^{-1}b^{10}}\left(\frac{d^2b^2}{a^2c^2}\right)^{-2}\left(c^2\left(\frac{1}{ab^2}\right)^{-3}\right)^4\right)^3$

$\left(\frac{b^2d^2}{a^2c^2}\right)^{-2}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(\frac{a}{b}\right)^{-c}=\left(\left(\frac{a}{b}\right)^{-1}\right)^c=\left(\frac{b}{a}\right)^c$
$=\left(\frac{a^2c^2}{b^2d^2}\right)^2$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$
$=\frac{\left(a^2c^2\right)^2}{\left(d^2b^2\right)^2}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a\cdot \:b\right)^n=a^nb^n$
$\left(d^2b^2\right)^2=\left(b^2\right)^2\left(d^2\right)^2$
$=\frac{\left(a^2c^2\right)^2}{\left(b^2\right)^2\left(d^2\right)^2}$
$=\frac{a^4c^4}{b^4d^4}$

$=\left(d^4a^3b^2c\frac{a^{-10}}{d^{-1}b^{10}}\cdot \frac{a^4c^4}{d^4b^4}\left(c^2\left(\frac{1}{ab^2}\right)^{-3}\right)^4\right)^3$

$\left(c^2\left(\frac{1}{ab^2}\right)^{-3}\right)^4$
$\left(\frac{1}{ab^2}\right)^{-3}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(\frac{a}{b}\right)^{-c}=\left(\left(\frac{a}{b}\right)^{-1}\right)^c=\left(\frac{b}{a}\right)^c$
$=\left(\frac{ab^2}{1}\right)^3$
$=\left(ab^2\right)^3$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a\cdot \:b\right)^n=a^nb^n$
$=a^3b^6$
$=\left(a^3b^6c^2\right)^4$
$=c^8a^{12}b^{24}$

$=\left(d^4a^{12}a^3b^{24}b^2c^8c\frac{a^{-10}}{d^{-1}b^{10}}\cdot \frac{a^4c^4}{d^4b^4}\right)^3$

$\frac{a^{-10}}{b^{10}d^{-1}}$
$=\frac{a^{-10}}{\frac{b^{10}}{d}}$
$=\frac{da^{-10}}{b^{10}}$
$=\left(d^4a^{12}a^3b^{24}b^2c^8c\frac{da^{-10}}{b^{10}}\cdot \frac{a^4c^4}{d^4b^4}\right)^3$$=\left(d^4a^{15}b^{26}c^9\frac{da^{-10}}{b^{10}}\cdot \frac{a^4c^4}{d^4b^4}\right)^3$
$=\left(da^9b^{12}c^{13}\right)^3$
$=d^3c^{39}a^{27}b^{36}$