Hola, necesito que me ayuden a resolver esta expresión, es de la reglas de leyes de exponentes?

Respuesta :

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%5E%7B4%7D%7D" />

Explicación paso a paso : Esta es mi propuesta de la solución.

1. - La expresión es : <img src="https://tex.z-dn.net/?f=%28%5Cfrac%7B2%5E%7B-1%7D%2A3%5E%7B1%2F4%7D%7D%7B2%5E%7B-3%7D%2A3%5E%7B1%2F2%7D%7D%29%5E%7B-2%7D" />

2.

- Recordando algunas propiedades básicas de los exponentes.

<img src="https://tex.z-dn.net/?f=a%5E%7Bm%7D%2Aa%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D%5C%5C%5C%5C%5Cfrac%7Ba%5E%7Bm%7D%7D%7Ba%5E%7Bn%7D%7D%3Da%5E%7Bm-n%7D%5C%5C%5C%5Ca%5E%7B-n%7D%3D%5Cfrac%7B1%7D%7Ba%5E%7Bn%7D%7D%5C%5C%5C%5C%28%5Cfrac%7Ba%7D%7Bb%7D%29%5E%7Bm%7D%3D%5Cfrac%7Ba%5E%7Bm%7D%7D%7Bb%5E%7Bm%7D%7D%5C%5C%5C%5Ca%5E%7B1%2Fn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D" />

3.

- Aplicando dichas propiedades y simplificando nos queda :

<img src="https://tex.z-dn.net/?f=%28%5Cfrac%7B2%5E%7B-1%7D%2A3%5E%7B1%2F4%7D%7D%7B2%5E%7B-3%7D%2A3%5E%7B1%2F2%7D%7D%29%5E%7B-2%7D%3D%5Cfrac%7B2%5E%7B%28-1%29%2A%28-2%29%7D%2A3%5E%7B%281%2F4%29%2A%28-2%29%7D%7D%7B2%5E%7B%28-3%29%2A%28-2%29%7D%2A3%5E%7B%281%2F2%29%2A%28-2%29%7D%7D%3D%5C%5C%5C%5C%3D%5Cfrac%7B2%5E%7B2%7D%2A3%5E%7B-1%2F2%7D%7D%7B2%5E%7B6%7D%2A3%5E%7B-1%7D%7D%3D2%5E%7B2%7D%2A2%5E%7B-6%7D%2A3%5E%7B-1%2F2%7D%2A3%5E%7B1%7D%3D%5C%5C%5C%5C%3D2%5E%7B2-6%7D%2A3%5E%7B-1%2F2%2B1%7D%3D2%5E%7B-4%7D%2A3%5E%7B1%2F2%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%5E%7B4%7D%7D" />

Saludos.