Monomial Factor with Exponents

Introduction to monomial factor with exponents:

"Monomial factor with exponent" means the monomial term with exponents need to factorise. Here we need to understand each and every terms.

From the term mono we can understand it is talking about a single term, so "monomial" means it is an algebraic expression which is having only one single term. We can also say that monomial is a product of numbers and variables, where variables can be any letter or a power of letter( power or index is called as exponents).Monomial can be a single letter or a number also.So, Monomial factor with exponents can be a single term consist of a number with variable and also with exponents and which can be factorise also. Here the factor means when we multiply two elements together we can get the final product.
Now we come to the term "Exponent" here it means the number can be multiply how many times which depends upon the power. Now we have a small idea about the term "Monomial factor with exponent".

Examples on Monomial Factor with Exponents:

1. 12x²

This a monomial, here we have one single term which is 12x². Here 12 is a number with a variable x having the power as 2. x² is  called  x to the second power. Here x is the base and 2 is the exponent.

2. -24abc

This is also a monomial having a single term. The exponent here is 1 for each variables.

Above are the examples of monomial with exponents.

Let us take an example and learn to facrorise:

1)12 x⁴

first we will find the factors of 12 which is

1 x 12

2 x 6

3 x 4

Now we will factor x² .This can be written as

x.x³

x^2.x²

x⁰.x⁴

As per the exponent law (a)^m.(a)ⁿ=a^m+n

so if we add the power we get the final results as x⁴.

2) 6a⁴b¹⁰= (2a³b²) .(  ? )

Here we need to find the missing terms. As we have already one part, to find the other part let us find the factor.

6.............can be written as

1 x 6

2 x 3

As we have already 2 in the question so we have to consider the factor for 6 as 2 x 3.

Now factor a⁴b¹⁰

a⁴=a¹.a³                           and  b¹⁰=b¹.b⁹

a⁴=a².a²                                    b¹⁰=b².b⁸

a⁴=a⁰.a⁴                                    b¹⁰=b³.b⁷

                                                     b¹⁰=b⁴.b⁶

                                                     b⁵=b⁵.b⁵

In the question we have a³b². so from the above factorisation we can find as the final results as 3ab⁸

^{Having problem with prime factorization chart 1-1000 keep reading my upcoming posts, i will try to help you.}

Conclusion on Monomial Factor with Exponents:

In monomial factor with exponents always we have to remember that whenever we multiply the monomials we add the exponents also. Degree of monomials is the sum of exponents of all the letters.