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
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
