How To Solve Negative Exponents

Before solving negative exponents , let’s have an overview of exponents followed by negative exponents examples
Exponents are one of the important algebraic operators that determines how many times a number is to be multiplied by itself. A number raised to an exponent can be shown as
number raised to exponent

where ‘X’ is the coefficient

a’ is the base

n’ is the exponent

The positive or negative signs of ‘n’ exponent indicate whether it is a positive exponent or negative exponent respectively. In the above expression , a is raised to a negative exponent. If it is written as
negative exponent

In this expression , a is raised to a negative exponent. Furthermore, we can write this expression as

negative exponents expression

For coefficient X=1 , the above equation becomes

solving negative equation

This implies that sign of an exponent can be changed by changing its position (either numerator or denominator) in the fraction line. Secondly , a number raised to a negative exponent ‘a-n ‘ is equivalent to its reciprocal ‘ 1/an ‘.

For n =2 , a = 2 , we have the above equation as

solving negative exponets equation

Negative Exponents Examples

The below given examples of negative exponents  will further tell you how to solve negative exponents
how to solve negative exponent example


By taking reciprocals of numbers raised to negative powers , we have positive exponents as

positive exponets

Expanding the numbers raised to positive exponents , we got

Expanding the numbers raised to positive exponents

As the numbers raised to zero exponents are equivalent to 1. So , we have the above equation as

answer to negative exponent

So , answer is 0.5


The square roots of numbers are equivalent to numbers raised to 1/2. So , we have
how to  solve negative exponents formula

By rearranging powers , we have

rearranging negative exponent formula

Expanding the powers , we got

expanding negative exponent formula

To solve the fractional exponent in (4)1/2 , we will first convert the base 4 to its exponential form

fractional exponent

Ian Roberts
San Francisco, USA

"If you're at school or you just deal with mathematics, you need to use This thing is really helpful."
Lisa Jordan
Math Teacher
New-York, USA

"I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. "
John Maloney
Student, Designer
Philadelphia, USA

" I'm a geek, and I love this website. It really helped me during my math classes. Check it out) "
Steve Karpesky
Vancuver, Canada

"I use a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"