Question

How do you multiply monomials with the same base?

Answer 1

Hint: The given question is related to the concept of polynomials. The sub-topic is monomial. Here, in this question we are asked how to multiply monomials which have the same base. A monomial is a polynomial containing one single term. In other words, a number, a variable or a product of a number and one or more variables is called a monomial.

Complete step by step answer:
The only rule of monomials is that the variables should be raised to only positive integer powers, not to the square roots or $\dfrac{1}{x}$ or any plus/minus signs. In order to multiply monomials, first we multiply the coefficients and then we multiply the variables by adding the exponents. When we have to multiply monomials with the same base, then we can directly add their exponents. This is shown in the following rule of exponent which is also called as the product of powers property.
$ \Rightarrow {a^m} \times {a^n} = {a^{m + n}}$
This can be much better explained with a help of an example.
Let${a^m} = {4^2}$and${a^n} = {4^3}$
Now, using the product of powers property, we have
$ \Rightarrow {4^2} \times {4^3} = {4^{2 + 3}} = {4^5}$
Thus, that’s how we multiply the monomials with the same base.

Note:The given question was very easy and basically theoretical. To explain better, we used an example. Students should know the concept of polynomials for better clarity and understanding of complex polynomial related questions. Students should also know about the different types of polynomials. Students should remember that monomials include numbers, whole numbers and variables. Fun fact-$\pi $ is a monomial.