Question

Solve for x: 2x^-2=4

Answer 1

`(√(2))/(2)`

Explanation:

First, we see that we have the term
`2x^(-2)` . When we have a negative exponent, we can always flip the number to its reciprocal and take the reciprocal to the positive exponent.

For example: here we have
`2x^(-2)` . To turn this into positive exponents, we now have:
`2*(1)/(x^2)` .

So, we have:
`2*(1)/(x^2)` = 4

Divide both sides by 4 and multiply both sides by x^2:

`x^(2) =1/2`

Square root both sides:

`x=√(1/2) =(√(2))/(2)`

Thus, the answer is
`(√(2))/(2)` .

Hope this helps!

Answer 2

`x=\sqrt{(1)/(2)},\:x=-\sqrt{(1)/(2)}`

Explanation:

Hey!!!

We first need to simplify:

`(2)/(x^2)=4`

`(2)/(x^2)x^2=4x^2`

`2=4x^2`

`x=\sqrt{(1)/(2)},\:x=-\sqrt{(1)/(2)}`

Hope this helps!!

:D