How to Solve Algebraic Equations With Double Exponents

••• Kelly Addison

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).

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About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.

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  • Kelly Addison

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