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
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
In this expression , a is raised to a negative exponent. Furthermore, we can write this expression as
For coefficient X=1 , the above equation becomes
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
Negative Exponents Examples
The below given examples of negative exponents will further tell you how to solve negative exponents
By taking reciprocals of numbers raised to negative powers , we have positive exponents as
Expanding the numbers raised to positive exponents , we got
As the numbers raised to zero exponents are equivalent to 1. So , we have the above equation as
So , answer is 0.5
The square roots of numbers are equivalent to numbers raised to 1/2. So , we have
By rearranging powers , we have
Expanding the powers , we got
To solve the fractional exponent in (4)1/2 , we will first convert the base 4 to its exponential form
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