Adding Negative Exponents

Introduction :

The term exponent in math is used to find the exponential value of the particular value it may be integer  or fraction . We can easy to get  the power of a  number using online calculator ,Consider  the unknown number , Here x is base and y is the power  of x

Adding Exponents means how many times to divide the number .

that is , `a ^(-n) = 1/a^n`

Steps for Adding Negative Exponents :

Negative exponents are added in the same way as the exponents are added with just a negative sign.

The given terms exponents are combined in a way such that the negative exponents are added or combined in case of same base.
In case of different bases , we have to simplify by convert it to positive exponent ,
Then we have to simplify the exponent value . Make the negative exponent to the positive one .
Now simplify further to get the results.
Ex  :   `5^-2 + 5^-4 = 5^((-2-4))`

`=5^-6`

=`1/5^6`

=`1/15625`

= 0.000064



Examples to Add Negative Exponents:

Ex 1:  A number  with negative exponents `8^(-3)`

Sol :     `8^(-3)` = `1/ (8^3)`

=`1/ (8 *8*8)`

= `1/ 512`

=0.00195

Ex 2:    Add the neagtive exponents` 7^-3`    + `5^-2`

Sol :    `=1/7^3 + 1/5^2`

`=1/343 +1/25`

=0.0029 +0.04

=0.0429

Ex 3:   Add the negative exponents `6^-2 + 6^-3`

Sol :  Using the rule , we have to add the exponents as 6 is the common base

= `6^(-2 + -3)`

` 6^(-2-3)`

=`6^-5`



= `1/(6^5)`

= 0.00012

Example 4:

Add the negative exponents  of `5^-3 +5^-5 +5^-2`

Solution:

Use the property to add the negative exponents , we have

=`5^-3 +5^-5 +5^-2`

=`5^(-3 + -5 + -2)`

=`5^(-3 -5 -2)`

= `5^-10`

= `1/(5^10)`

=0.04832

Example 5:

Add the negative exponents  of` 3^-3 + 3^-6`

Solution:

Use `a^-n = 1/a^n`   rule

We  get ,

=`1/3^3 +1/3^6`

=0.03703 +0.0013

=0.03833

Example 6:

Add the negative exponents  of `5^-2 + 5^-3`

Solution:

Use a ^-n = 1/a^n

Then we  get ,

=`1/5^2 +1/5^3` 

=0.04+0.008

=0.048

Practice Problem to Add Negative Exponents:

Pro1 : Add the negative exponents  of` 2^-2 +2^-4`

Ans : 0.3125

Pro2 :Add the negative exponents  of` 3^-3 +3^-2`

Ans : 0.1481