Question

Escribe la potencia que falta
1/8 =2 =
1/81 =9 =
1/25 =5 =
1/10000 =10 =

Answer 1

¡Hola ^^!

⚠️ Recordemos la siguiente propiedad ⚠️

$\boxed{ \frac{1}{a} = {a}^{ - 1} }$


Resolver:
1)
$\frac{1}{8} = {2}^{x} \\ \\ \frac{1}{ {2}^{3} } = {2}^{x} \\ \\ {2}^{ - 3} = {2}^{x} \\ \\ \boxed{x = - 3}$

2.
$\frac{1}{81} = {9}^{x } \\ \\ \frac{1}{ {9}^{2} } = {9}^{x} \\ \\ {9}^{ - 2} = {9}^{x} \\ \\ \boxed{x = - 2 }$

3.
$\frac{1}{25} = {5}^{x} \\ \\ \frac{1}{ {5}^{2} } = {5}^{x} \\ \\ {5}^{ - 2} = {5}^{x} \\ \boxed{x = - 2}$

4.
$\frac{1}{10000} = {10}^{x} \\ \\ \frac{1}{ {10}^{4} } = {10}^{x} \\ \\ {10}^{ - 4} = {10}^{x} \\ \boxed{x = - 4}$

Espero que te sirva de ayuda ^u^

Saludos:
Margareth ✌️