Question

How do you simplify ${({x^3})^2}$?

Answer 1

Hint: Exponential functions have the form $f(x) = {b^x}$, where b is greater than x=zero, that is positive and b is not equal to one. Just as in any exponential expression, b is called the base of that function, and x is called the exponent of that function. In any exponential question, we have to consider exponential formulas to solve it.

Complete step by step solution:
According to the question we have to simplify the term ${({x^3})^2}$
So to solve these types of questions we can use the exponential formula
$ \Rightarrow {a^m} \times {a^n} = {a^{m + n}}$
Where $a$ is the base and m and n are the power of the base.
So in the question, we have ${({x^3})^2}$ which can be written as
$ \Rightarrow {x^3} \times {x^3}$
So, we have converted it into the form that we have discussed above.
Now, by using that formula we can simplify the equation as shown
$ \Rightarrow {x^3} \times {x^3} = {x^{3 + 3}} = {x^6}$
Hence, after simplifying the equation we get x raised to the power of six
We can also solve it by using another exponential formula which is
$ \Rightarrow {({a^m})^n} = {a^{m \times n}}$
So, we can solve it with this formula as
$ \Rightarrow {({x^3})^2} = {x^{3 \times 2}} = {x^6}$

Hence, after simplifying we again get the equation we get x raised to the power of six.

Note:
We can clearly observe that we have multiple ways to proceed in any exponential question for simplifying it. We have to be aware of when we have to add powers and when we have to multiply the powers of any base while solving it. There is a great chance of making mistakes in doing addition or subtraction of powers of the exponential function.