Question

How do you simplify ${\left( {{t^3}} \right)^2}$?

Answer 1

Hint: In order to determine the value of the above question ,use exponent property . But the question arises what is exponent , so the answer to this is that the base $'a'$ raised to the power of n is equal to the multiplication of ‘a’ , n times. \[{a^{\;n}}\; = \;a\; \times \;a\; \times \;...\; \times \;a\]…..up to n times.
Power rule of exponent will provide us the more simplified form of our question as power rule states that when a power is raised to a power of a number then the exponents get multiplied with each other and makes the solution easier and way shorter.
${\left( {{a^n}} \right)^m} = {a^{m \times n}}$

Complete step by step answer:
We are given an exponent number ${\left( {{t^3}} \right)^2}$
To solve the given question, we must know the properties of exponents and with the help of them we are going to rewrite our question.
In order to simplify our exponent value, we’ll use one of the important property of exponent which is known as Power rules which states “a power raised to a power for number, is equal to the multiplication of the exponents as given below”
${\left( {{a^n}} \right)^m} = {a^{m \times n}}$
Applying the above power rule in this question, considering $a = t,n = 3,m = 2$ we get:
$
   \Rightarrow {t^{3 \times 2}} \\
   \Rightarrow {t^6} \\
 $
Therefore, simplification of ${\left( {{t^3}} \right)^2}$ is equal to ${t^6}$.

Note: Don’t forget to cross check your result. Any number raised to the power of ‘1’ is always equal to the number itself. Any number raised to the power of ‘0’ is always equal to the number ‘1’. The number one raised to any power is always ‘1’.