Question

doy coronita quien me ayude
procedimiento quiero​

Answer 1

Verified answer

RESOLVER:

PRIMER PUNTO:

a) [tex]\left(5^3\cdot \:2^2\cdot \:4^3\right)^2[/tex]

[tex]=\left(5^3\right)^2\cdot \left(2^2\right)^2\cdot \left(4^3\right)^2[/tex]

[tex]=15625\cdot \:16\cdot \left(4^3\right)^2[/tex]

[tex]=15625\cdot \:16\cdot \:4^{3\cdot \:2}[/tex]

[tex]=15625\cdot \:16\cdot \:4^6[/tex]

[tex]=15625\cdot \:16\cdot \:4096[/tex]

[tex]\boxed{=1024000000}[/tex]

b) [tex]3^2\cdot \:3^3\left(\frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}\right)[/tex]

[tex]=3^2\cdot \:3^3\cdot \frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}[/tex]

[tex]=243\cdot \frac{3^3\cdot \:3^4}{3^4\cdot \:3^2}[/tex]

[tex]=\frac{3^3\cdot \:3^4\cdot \:243}{3^4\cdot \:3^2}[/tex]

[tex]=\frac{3^3\cdot \:243}{3^2}[/tex]

[tex]=243\cdot \:3^{3-2}[/tex]

[tex]=3\cdot \:243[/tex]

[tex]\boxed{=729}[/tex]

c) [tex]\left(\frac{3\cdot \:2^3}{2^2\cdot \:3^2}\right)^2[/tex]

[tex]=\frac{\left(3\cdot \:2^3\right)^2}{\left(2^2\cdot \:3^2\right)^2}[/tex]

[tex]=\frac{576}{\left(2^2\cdot \:3^2\right)^2}[/tex]

[tex]=\frac{576}{1296}[/tex]

[tex]\boxed{=\frac{4}{9}}[/tex]

SEGUNDO PUNTO:

a) [tex]\left(5^2\right)^3[/tex]

[tex]=5^{2\cdot \:3}[/tex]

[tex]\boxed{5^6=15625}[/tex]

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

[tex]=\left(\frac{3}{7}\right)^{2\cdot \:5}[/tex]

[tex]\boxed{=\left(\frac{3}{7}\right)^{10}=\frac{59049}{282475249}}[/tex]

c) [tex]\left(\frac{4}{5}\right)^4[/tex]

[tex]=\frac{4^4}{5^4}[/tex]

[tex]\boxed{=\frac{256}{625}}[/tex]

TERCER PUNTO:

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

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

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

[tex]=1\cdot \:3[/tex]

[tex]\boxed{3}[/tex]

b) [tex]\frac{\left(\sqrt{49}\sqrt{49}\sqrt{49}\sqrt{49}\right)^2}{\left(\left(\sqrt{49}\right)^2\right)^3}[/tex]

[tex]=\frac{\left(49^{4\cdot \frac{1}{2}}\right)^2}{\left(\left(\sqrt{49}\right)^2\right)^3}[/tex]

[tex]=\frac{\left(49^{4\cdot \frac{1}{2}}\right)^2}{49^3}[/tex]

[tex]=\frac{49^4}{49^3}[/tex]

[tex]=49^{4-3}[/tex]

[tex]\boxed{49}[/tex]

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

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

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

[tex]\boxed{=1000000}[/tex]

d) [tex]\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}}[/tex]

[tex]=\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}}[/tex]

[tex]=\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}}[/tex]

[tex]=\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}[/tex]

[tex]=\frac{10^2\cdot \:10^2\cdot \:10^3\left(3^2+1\right)}{22\cdot \:10^3}[/tex]

[tex]=\frac{5000\left(3^2+1\right)}{11}[/tex]

[tex]\boxed{=\frac{50000}{11}}[/tex]

[tex]Buena\:suerte\:con\:tus\:tareas\::ProfeAndresFelipe :)[/tex]