Negative Exponents


It determines how many times a number is to be divided.

Formula for Negative Exponents

The general formula for negative exponents is

negative exponents formula

where n is the positive exponent and -n is the negative exponent with base a .

Description

Negative exponents are easy way to convert division problems into multiplication problems as numbers can be presented in powers of decimal or fraction without need to write them in decimal or fraction forms respectively. The above formula says a negative exponent can be converted into positive by changing its position in fractional line i.e. moving the exponents present in numerator to denominator or vice versa.

Rules for negative exponents

The below rules are applicable for all negative fractional exponents or non-fractional exponents

1.Convert the negative exponent number into positive exponent number by taking its reciprocal

2.Solve the positive exponent number

3.Subtract the exponents with similar base in both numerator and denominator and add the exponents with similar base in both numerator and denominator

Simplifying Negative Exponents

Let’s use the above rules to solve the following examples

Simplifying Negative Exponents

Solution

a. Taking reciprocal of the given expression [Rule 1] , we have
Taking reciprocal of the given expression Rule 1

b. Simplifying the positive exponent [Rule 2] , we have
Simplifying the positive exponent Rule 2

Answer is 0.25

answer for negative exponent

Solution

a. Taking reciprocal of the given expression [Rule 1] , we have

Taking reciprocal of the given expression

b.Simplifying the positive exponent [Rule 2] , we have
simplifying the positive exponent

Answer is 0.5


Dividing negative exponents

Exponents having same base are subtracted in division and added in multiplication
exponents are substracted

Solution

a. Taking reciprocal of the given expression [Rule 1] , we have
implementation of Rule 3

b. Implementing Rule 3 , we got
reciprocal of negative exponent
Answer is 0.5



Ian Roberts
Engineer
San Francisco, USA

"If you're at school or you just deal with mathematics, you need to use Studygeek.org. 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
Bookkeeper
Vancuver, Canada

"I use Studygeek.org 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"