How do you simplify $ {(4{x^3})^2} $ ?

Hint: Here we will take the given expression and will apply the laws of power and exponent and will simplify the solution. Also, we will use the square concepts during the solution.

Complete step-by-step answer:
Take the given expression: $ {(4{x^3})^2} $
Since the power is outside the bracket, so power is applied to all the terms inside the bracket.
 $ {(4{x^3})^2} = {4^2}.{({x^3})^2} $
Here we will use the power of product rule which states that when there is power to power then they are multiplied with each other.
 $ {(4{x^3})^2} = {4^2}.({x^6}) $
Now, we will apply the square concepts where the term is multiplied with itself twice.
 $ {(4{x^3})^2} = 4.4.({x^6}) $
Simplify the above equation-
 $ {(4{x^3})^2} = 16.({x^6}) $
The above equation can be re-written as –
 $ {(4{x^3})^2} = 16{x^6} $
This is the required solution.
So, the correct answer is “$16{x^6} $ ”.

Note: Remember different identities to solve and always remember when there is power outside the bracket, then the power is applied to all the terms inside the bracket. Know the concepts of squares and square-root and apply accordingly. Square is the number multiplied itself.