Question

32 elevado a la 8 por 16 elevado a la 10 entre 8 elevado a la 25

Answer 1

Respuesta:

$\frac{32^8\cdot \:16^{10}}{8^{25}}\\\\\mathrm{Factorizar\:}32=2^5==\left(2^5\right)^8\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a^b\right)^c=a^{bc}\\\\=2^{5\cdot \:8}=2^{40}\\\\\mathrm{Factorizar\:}8=2^3==\left(2^3\right)^{25}\\\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a^b\right)^c=a^{bc}\\\\=2^{3\cdot \:25}=2^{75}\\\\\mathrm{Factorizar\:}16=2^4==\left(2^4\right)^{10}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \left(a^b\right)^c=a^{bc}\\\\=2^{4\cdot \:10}=2^{40}\\\\=\frac{2^{40}\cdot \:2^{40}}{2^{75}}\\\\2^{40}\cdot \:2^{40}\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\\=2^{40+40}=2^{80}\\\\=\frac{2^{80}}{2^{75}}$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\=2^{80-75}=2^5\\\\2^5=32\\\\\frac{32^8\cdot \:16^{10}}{8^{25}}=32$