In your algebra classes, you will often have to solve equations with exponents. Sometimes, you may even have double exponents, in which an exponent is raised to another exponential power, as in the expression (x^a)^b. You will be able to solve these, as long as you correctly utilize the properties of exponents and apply the properties of algebraic equations that you have been using in your class all along.
Simplify the equation as much as possible. If you have the equation (x^2)^2+2^2=3*4, simplify all of the numbers to obtain (x^2)^2+4=12.
Resolve the double exponential. A fundamental property of exponentials is that (x^a)^b=x^ab, so (x^2)^2=x^4.
Isolate the double exponential on one side of the equation. You must subtract 4 from both sides of the equation, to obtain x^4=8.
Take the fourth root of both sides of the equation, to obtain x with no exponentials. Doing so, you will obtain x=fourthroot(8), or x= -fourthroot(8).
- Kelly Addison