Question

Express the prime factorization of the numbers in exponential form.

Answer 1

Hint:Here in the given question we need to know and understand about prime factorization and its representation in exponential form. To find out this firstly we need to find the prime factors of the given number and then arrange them in a row. Now if there are repeated prime factors we need to represent them as exponents because this makes the simplification more clear and understandable.

Complete step by step answer:
We know that prime numbers are a set of numbers which have their factor as 1 and the number itself and thus all the prime numbers have only two factors only. Prime factorization is a process of splitting the given numbers into a product of prime factors; we know that in this process the prime factors may repeat more than one time. When we write these numbers as a product of the prime numbers the repeated prime factors can be clubbed and written in an exponential form.

Considering an example as 24 we will first express the prime factors of 24.
\[ \Rightarrow \]\[24 = 2 \times 2 \times 2 \times 3\]
Now has we can see that prime factors are repeated which can be represented as exponents of that prime factors as follows
\[ \Rightarrow \]\[24 = {2^3} \times 3\]
Here we can see that prime factor 2 is raised to the power 3, which indicates that 2 is repeated 3 times. In this way it is appropriate way to represent the prime factors in an exponential form

Note: Remember any number that is in exponential form should be represented as \[{m^n}\]here n is the exponent and m is the base. The exponent here indicates the number of times the base should be multiplied. When two or more numbers are expressed in exponential form, we can simplify them using laws of exponents.