SOLUTION: How do you solve: x^-2=9

Question 69787: How do you solve:
x^-2=9
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Your problem is:

The negative exponent means that the term raised to that negative value can be changed
into a fraction having 1 as the numerator and the term with a positive exponent as the
denominator. Easier to show by an example than to explain it.
Think "I can change into by making the denominator
of a fraction that has 1 as its numerator." When you do that your problem becomes:

Then you can eliminate the denominator if you multiply both sides by
If you do that multiplication on the left side you have a fraction that has
in both the numerator and denominator. This is equivalent to 1. On the right side the multiplication results in and the problem becomes:

Dividing both sides by 9 gives:

Now just take the square root of both sides. Notice that because
. Also notice that both the positive and negative forms
of are needed because when either is squared they produce a positive value
of
The two answers to this problem are:
and
You can check this by putting each of these answers (positive and negative) one at a time
into the equation:

and see that with these values the left side of the equation equals 9.

RELATED QUESTIONS
How do do you solve... (answered by KMST)

How do you solve 2/x^2 + 9/x = 0 (answered by savvyhush23)

How do you solve:... (answered by stanbon)

how do you solve... (answered by jim_thompson5910)

How do you solve... (answered by Earlsdon,oberobic)

how do you solve for... (answered by jsmallt9)

how do you solve... (answered by rothauserc)

Hi, how do you solve log6 9 + log6 x =... (answered by MathLover1)

how do you solve... (answered by stanbon)