Question 285143
{{{2x^(-1/2)=8}}}
We start by isolating the base and its exponent. So we'll get rid of the 2 by dividing both sides by 2:
{{{x^(-1/2)=4}}}
From here there are several ways to go. Probably the fastest is base on the idea that we want x to have an exponent of 1. So how can we change an exponent from -1/2 to 1? One way would be to raise both sides of the equation to the -2 power. (You'll see why this works as we do it.)
{{{(x^(-1/2))^(-2)=(4)^(-2)}}}
On the left side the rule for the exponents is to multiply them. And what do you get when you multiply -1/2 and -2? Answer: 1! You <b>always</b> get a 1 when you multiply reciprocals! So now we have:
{{{x = (4)^(-2)}}}
Now we just have to simplify the right side:
{{{x = (4)^(-2) = 1/(4^2) = 1/16}}}