Question

ayuda con la 6 pero el literal b

Answer 1

Respuesta:

$=\frac{2^{76}}{5^{34}}$

Explicación paso a paso:

$\frac{\left(\frac{4}{5}\right)^4\cdot \left(\frac{4}{5}\right)^7\cdot \left(\frac{4}{5}\right)^{10}}{\left(\frac{5}{8}\right)^8\div \left(\frac{4}{5}\right)^5}$

$\frac{\left(\frac{4}{5}\right)^4\left(\frac{4}{5}\right)^7\left(\frac{4}{5}\right)^{10}}{\frac{\left(\frac{5}{8}\right)^8}{\left(\frac{4}{5}\right)^5}}\\\\Bases\ iguales\ los\ exponentes\ se\ suman:$

$=\frac{\left(\frac{4}{5}\right)^{21}}{\frac{\left(\frac{5}{8}\right)^8}{\left(\frac{4}{5}\right)^5}}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\\\\=\frac{\left(\frac{4}{5}\right)^{21}\left(\frac{4}{5}\right)^5}{\left(\frac{5}{8}\right)^8}\\\\=\frac{\left(\frac{4}{5}\right)^{26}}{\left(\frac{5}{8}\right)^8}\\\\=\frac{\left(\frac{4}{5}\right)^{26}}{\frac{5^8}{8^8}}$

$=\frac{\frac{4^{26}}{5^{26}}}{\frac{5^8}{8^8}}$

$=\frac{4^{26}\cdot \:8^8}{5^{26}\cdot \:5^8}$

$=\frac{4^{26}\cdot \:8^8}{5^{34}}\\\\\\Simplificamos:$

$=\frac{2^{76}}{5^{34}}$