Question

ayuda por favor.........​

Answer 1

Respuestas y pasos:

1)  $\frac{\left[\left(-2\right)^2\right]^3\cdot \left[\left(-3\right)^4\right]^5\cdot \left(2^5\right)^3\cdot \left[\left(-2\right)^5\right]^2}{\left[\left(-2\right)^7\right]^2\cdot \left(\left(-3\right)^{10}\right)\cdot \left(-3\right)^9\cdot \left(2^4\right)}$

Desarrollar por partes:

$\left(\left(-2\right)^2\right)^3\left(\left(-3\right)^4\right)^5\cdot \left(2^5\right)^3\left(\left(-2\right)^5\right)^2=128^3\cdot \left(3^4\right)^5\cdot \left(2^5\right)^2$

$=\frac{128^3\left(3^4\right)^5\left(2^5\right)^2}{\left(-3\right)^{10}\left(-3\right)^9\cdot \:2^4\left(\left(-2\right)^7\right)^2}$

$\left(\left(-2\right)^7\right)^2\left(-3\right)^{10}\left(-3\right)^9\cdot \:2^4=-3^{19}\cdot \:2^4\cdot \left(2^7\right)^2$

$=\frac{128^3\left(3^4\right)^5\left(2^5\right)^2}{-3^{19}\cdot \:2^4\left(2^7\right)^2}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{a}{-b}=-\frac{a}{b}$

$=-\frac{128^3\left(3^4\right)^5\left(2^5\right)^2}{\left(2^7\right)^2\cdot \:3^{19}\cdot \:2^4}$

$\mathrm{Cancelar\:}\frac{128^3\cdot \left(3^4\right)^5\cdot \left(2^5\right)^2}{\left(2^7\right)^2\cdot \:3^{19}\cdot \:2^4}$

$=-\frac{2^{17}\cdot \:3\left(2^5\right)^2}{\left(2^7\right)^2}$

$\left(2^7\right)^2=2^{14}$

$=-\frac{2^{17}\cdot \:3\left(2^5\right)^2}{2^{14}}$

$\left(2^5\right)^2=2^{10}$

$=-\frac{2^{17}\cdot \:2^{10}\cdot \:3}{2^{14}}$

$2^{17}\cdot \:3\cdot \:2^{10}=2^{27}\cdot \:3$

$=-\frac{2^{27}\cdot \:3}{2^{14}}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{2^{27}}{2^{14}}=2^{27-14}$

$=3\cdot \:2^{27-14}$

$\mathrm{Restar:}\:27-14=13$

$=-2^{13}\cdot \:3$

$=-8192\cdot \:3$

$=-24576$

2) $\left(\frac{2^2\cdot 3^5\cdot 2^{10}\cdot 3^4\cdot 5}{5\cdot 3^3\cdot 3^2\cdot 2^{11}}\right)^2=$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{\left(2^2\cdot \:3^5\cdot \:2^{10}\cdot \:3^4\cdot \:5\right)^2}{\left(5\cdot \:3^3\cdot \:3^2\cdot \:2^{11}\right)^2}$

$\left(2^2\cdot \:3^5\cdot \:2^{10}\cdot \:3^4\cdot \:5\right)^2=1.62496\:x\:10^{17}$

$=\frac{1.62496\:x 10^{17}}{\left(5\cdot \:3^3\cdot \:3^2\cdot \:2^{11}\right)^2}$

$\left(5\cdot \:3^3\cdot \:3^2\cdot \:2^{11}\right)^2=6191736422400$

$=\frac{1.62496\:x 10^{17}}{\left6191736422400}$

$Dividir$

$=26244$

3) $\left[\frac{3^5\cdot \left(-4\right)^2\cdot \left(-7\right)^3\cdot \left(-4\right)^5\cdot \left(-7\right)^7}{\left(-7\right)\cdot \left(-4\right)^6\cdot \left(-7\right)^9\cdot \left(3\right)}\right]^3$

$=\frac{\left(3^5\left(-4\right)^2\left(-7\right)^3\left(-4\right)^5\left(-7\right)^7\right)^3}{\left(-7\left(-4\right)^6\left(-7\right)^9\cdot \:3\right)^3}$

$\left(3^5\left(-4\right)^2\left(-7\right)^3\left(-4\right)^5\left(-7\right)^7\right)^3=7^{21}\cdot \:4^{15}\cdot \:2.37171\:x10^{18}$

$=\frac{7^{21}\cdot \:4^{15}\cdot \:2.37171\:x 10^{18}}{\left(-7\left(-4\right)^6\left(-7\right)^9\cdot \:3\right)^3}$

$\left(-7\left(-4\right)^6\left(-7\right)^9\cdot \:3\right)^3=-7^{27}\cdot \:4^{18}\cdot \:9261$

$=\frac{7^{21}\cdot \:4^{15}\cdot \:2.37171\:x10^{18}}{-7^{27}\cdot \:4^{18}\cdot \:9261}$

$=\frac{7^{21}\cdot \:4^{15}\cdot \:2.56096\:x 10^{14}}{7^{27}\cdot \:4^{18}}$

$=-\frac{2.56096\:x 10^{14}}{7^6\cdot \:4^3}$

$Dividir:$

$=-34012224$

4) $\left(\frac{\left(2\right)^4\cdot \left[\left(-5\right)^5\right]^4\cdot \left[\left(-10\right)^5\right]^6\cdot \left(-10\right)^5\cdot \left(-5\right)^8}{2^4\cdot \left[\left(-5\right)^5\right]^5\cdot \left(-10\right)^{35}}\right)^4$

$\frac{2^4\left(\left(-5\right)^5\right)^4\left(\left(-10\right)^5\right)^6\left(-10\right)^5\left(-5\right)^8}{2^4\left(\left(-5\right)^5\right)^5\left(-10\right)^{35}}=-5^3$

$=\left(-5^3\right)^4$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(-a\right)^n=a^n,\:\mathrm{si\:}n\mathrm{\:es\:par}$

$=\left(5^3\right)^4$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a^b\right)^c=a^{bc}$

$=5^{3\cdot \:4}$

$=5^{12}$

$=244140625$