How do you solve x to the power of negative half equals 1 and what do you have to do when you move the negative power of a half to the other side?

Answer 1

You never "move" things "to the other side" of an equation. The only

permissible treatment of an equation is to perform the same operation

on both sides.

Let's have a look at this one:

(x)-0.5 = 1

A negative exponent means the reciprocal of the positive one,

so you can write:

1/(x)0.5 = 1

You haven't changed anything or performed any operation, only

written the left side in a different way.

Now it's time to think about the meaning of an exponent of 1/2 .

It means "square root", so there's another way to write the left side:

1/sqrt(x) = 1

We still haven't performed any operations, only found different ways

to write the left side. Now we can do some operations to solve for 'x'.

Multiply each side of the equation by sqrt(x):

1 = sqrt(x)

Square both sides of the equation:

1 = x

What was so mysterious or complicated about that ?