Question

$^{3} \sqrt{-8}$ $^{3} \sqrt{81}$ $^{5} \sqrt{-32}$

Answer 1

Respuesta:

la respuesta es $=22674816$

Explicación paso a paso:

$^{3} \sqrt{-8}^{3} \sqrt{81}^{5} \sqrt{-32}$

$\left(\sqrt{-8}\right)^3=2^4\sqrt{2}i^3\\=2^4\cdot \:3\sqrt{2}\sqrt{-32}i^3\left(\sqrt{81}\right)^5\\\left(\sqrt{81}\right)^5=59049\\=2^4\cdot \:3\cdot \:59049\sqrt{2}\sqrt{-32}i^3\\\sqrt{-32}=4\sqrt{2}i\\=2^4\cdot \:3\cdot \:59049\cdot \:4\sqrt{2}\sqrt{2}i^3i\\=3i^3\cdot \:2^4\sqrt{2}\cdot \:59049i2^2\sqrt{2}\\=3i^3\sqrt{2}\cdot \:59049i2^{4+2}\sqrt{2}\\=3i^3\sqrt{2}\cdot \:59049i2^6\sqrt{2}\\=2^6\cdot \:3\cdot \:59049\cdot \:2i^3i\\=3\cdot \:59049i^{3+1}\cdot \:2^6\cdot \:2$

$=2^6\cdot \:354294i^4\\i^4=1\\=2^6\cdot \:354294\cdot \:1\\=354294\cdot \:1\cdot \:64\\=22674816$