Question

Me podrían ayudar? por favor!, es de matemática.
Tema: Potenciación de números racionales.
No respondas si no sabes, gracias!

Answer 1

Respuesta:

$=\frac{8281}{576}$

Explicación paso a paso:

minimo comun denominador 7/2

$=\frac{\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}\left(\left(\frac{1}{25}\right)^0\right)^{\frac{1}{2}}}{\sqrt{\left(\frac{7}{2}\right)^8}\left(\frac{2}{6}+\frac{3}{4}\right)^{13}}$

$=\frac{1^{\frac{1}{2}}\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}}{\sqrt{\left(\frac{7}{2}\right)^8}\left(\frac{2}{6}+\frac{3}{4}\right)^{13}}$

$=\frac{\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}}{\sqrt{\left(\frac{7}{2}\right)^8}\left(\frac{2}{6}+\frac{3}{4}\right)^{13}}$

$=\frac{\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}}{\frac{13^{13}}{12^{13}}\sqrt{\left(\frac{7}{2}\right)^8}}$

$=\frac{\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}}{\frac{13^{13}}{12^{13}}\sqrt{\left(\frac{7}{2}\right)^8}}$

$=\frac{\left(\left(\frac{2}{7}\right)^{-3}\right)^2\left(\left(\frac{12}{13}\right)^3\right)^{-5}}{\frac{7^4}{2^4}\cdot \frac{13^{13}}{12^{13}}}$

$=\frac{\frac{13^{15}\cdot \:117649}{2^{36}\cdot \:14348907}}{\frac{7^4}{2^4}\cdot \frac{13^{13}}{12^{13}}}$

$\frac{117649\cdot \:13^{15}}{2^{36}\cdot \:14348907\cdot \frac{13^{13}}{12^{13}}\cdot \frac{7^4}{2^4}}$

$=\frac{13^{15}\cdot \:117649}{2^{36}\cdot \:14348907\cdot \frac{2401}{16}\cdot \frac{13^{13}}{12^{13}}}$

$=\frac{13^{15}\cdot \:117649}{13^{13}\cdot \:1382976}$

$=\frac{13^{15}\cdot \:49}{13^{13}\cdot \:576}$

$=\frac{49\cdot \:13^{15-13}}{576}$

$=\frac{13^2\cdot \:49}{576}$

$=\frac{8281}{576}$