Question

doy coronita quien me ayude
procedimiento quiero​

Answer 1

RESOLVER:

PRIMER PUNTO:

a) $\left(5^3\cdot \:2^2\cdot \:4^3\right)^2$

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

$=15625\cdot \:16\cdot \left(4^3\right)^2$

$=15625\cdot \:16\cdot \:4^{3\cdot \:2}$

$=15625\cdot \:16\cdot \:4^6$

$=15625\cdot \:16\cdot \:4096$

$\boxed{=1024000000}$

b) $3^2\cdot \:3^3\left(\frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}\right)$

$=3^2\cdot \:3^3\cdot \frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}$

$=243\cdot \frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}$

$=\frac{3^3\cdot \:3^4\cdot \:243}{3^4\cdot \:3^2}$

$=\frac{3^3\cdot \:243}{3^2}$

$=243\cdot \:3^{3-2}$

$=3\cdot \:243$

$\boxed{=729}$

c) $\left(\frac{3\cdot \:2^3}{2^2\cdot \:3^2}\right)^2$

$=\frac{\left(3\cdot \:2^3\right)^2}{\left(2^2\cdot \:3^2\right)^2}$

$=\frac{576}{\left(2^2\cdot \:3^2\right)^2}$

$=\frac{576}{1296}$

$\boxed{=\frac{4}{9}}$

SEGUNDO PUNTO:

a) $\left(5^2\right)^3$

$=5^{2\cdot \:3}$

$\boxed{5^6=15625}$

b) $\left[\left(\frac{3}{7}\right)^2\right]^5$

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

$\boxed{=\left(\frac{3}{7}\right)^{10}=\frac{59049}{282475249}}$

c) $\left(\frac{4}{5}\right)^4$

$=\frac{4^4}{5^4}$

$\boxed{=\frac{256}{625}}$

TERCER PUNTO:

a) $\sqrt[3]{\frac{81}{3}}\cdot \:3^4\cdot \frac{1}{3^4}$

$=\frac{1\cdot \sqrt[3]{\frac{81}{3}}\cdot \:3^4}{3^4}$

$=1\cdot \sqrt[3]{\frac{81}{3}}$

$=1\cdot \:3$

$\boxed{3}$

b) $\frac{\left(\sqrt{49}\sqrt{49}\sqrt{49}\sqrt{49}\right)^2}{\left(\left(\sqrt{49}\right)^2\right)^3}$

$=\frac{\left(49^{4\cdot \frac{1}{2}}\right)^2}{\left(\left(\sqrt{49}\right)^2\right)^3}$

$=\frac{\left(49^{4\cdot \frac{1}{2}}\right)^2}{49^3}$

$=\frac{49^4}{49^3}$

$=49^{4-3}$

$\boxed{49}$

c) $\frac{10^2\cdot \:10^3\sqrt[3]{1000}\cdot \:10^4}{\left(\sqrt[4]{10000}\sqrt[3]{1000}\right)^2}$

$=\frac{10^2\cdot \:10^3\cdot \:10\cdot \:10^4}{\left(\sqrt[4]{10000}\sqrt[3]{1000}\right)^2}$

$=\frac{10^{10}}{\left(\sqrt[4]{10000}\sqrt[3]{1000}\right)^2}$

$\boxed{=1000000}$

d) $\frac{\left(8+2\right)^2\left(12-2\right)^2\cdot \:10^3\left(3^2+1\right)}{\left(20+2\right)\sqrt{100}\sqrt[3]{1000}\sqrt[4]{10000}}$

$=\frac{\left(8+2\right)^2\left(12-2\right)^2\cdot \:10^3\left(3^2+1\right)}{\left(20+2\right)\cdot \:10\sqrt[3]{1000}\sqrt[4]{10000}}$

$=\frac{\left(8+2\right)^2\left(12-2\right)^2\cdot \:10^3\left(3^2+1\right)}{\left(20+2\right)\cdot \:10\cdot \:10\sqrt[4]{10000}}$

$=\frac{\left(8+2\right)^2\left(12-2\right)^2\cdot \:10^3\left(3^2+1\right)}{\left(20+2\right)\cdot \:10\cdot \:10\cdot \:10}$

$=\frac{10^2\cdot \:10^2\cdot \:10^3\left(3^2+1\right)}{22\cdot \:10^3}$

$=\frac{5000\left(3^2+1\right)}{11}$

$\boxed{=\frac{50000}{11}}$

$Buena\:suerte\:con\:tus\:tareas\::ProfeAndresFelipe :)$