Si : x ^ - n = 8Reducir : 64x ^ 2n + x ^ - 2n?

Si <img src="https://tex.z-dn.net/?f=%20x%5E%7B-n%7D%20%3D8" /> , Reducir<img src="https://tex.z-dn.net/?f=64%20x%5E%7B2n%7D%20%2B%20x%5E%7B-2n%7D%20" />

Primero arreglaremos la condición :

<img src="https://tex.z-dn.net/?f=%20x%5E%7B-n%7D%20%3D8" />

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%5E%7Bn%7D%7D%20%3D8" />

<img src="https://tex.z-dn.net/?f=1%3D8%28x%5E%7Bn%7D%29" />

Teniendo eso en cuenta, procedemos a desarrollar :

<img src="https://tex.z-dn.net/?f=64%20x%5E%7B2n%7D%20%2B%20x%5E%7B-2n%7D%20" />

<img src="https://tex.z-dn.net/?f=%288%29%5E%7B2%7D%20%28x%5E%7B2n%7D%29%20%2B%20x%5E%7B-2n%7D%20" />

<img src="https://tex.z-dn.net/?f=8%2A8%2Ax%5E%7Bn%7D%2Ax%5E%7Bn%7D%2B%20x%5E%7B-2n%7D" />

<img src="https://tex.z-dn.net/?f=1%2B%20x%5E%7B-2n%7D" />

<img src="https://tex.z-dn.net/?f=1%2B%20%5Cfrac%7B1%7D%7Bx%5E%7B2n%7D%7D" />

[img = 10]

[img = 11]

[img = 12]

[img = 13]

[img = 14]

[img = 15]

[img = 16]

[img = 17]

[img = 18].