How do you simplify \[{{\left( \dfrac{4x}{3y} \right)}^{2}}\]?

Hint: In this problem, we have to simplify the given fraction. We are given a whole square fraction. We have to square each term in the numerator and the denominator, to get a simplified form. We also know how to square the numbers we should square each term using multiplication tables to get a simplified form. We know that 4 square gives 16 and 3 square gives 9 and if we square any variable, we can get the squared term of the variable and substituting in the given problem, we will get the required result.

Complete step by step solution:
We know that the given expression to be simplified is
\[{{\left( \dfrac{4x}{3y} \right)}^{2}}\]
Now we can square the numerator and the denominator.
\[\Rightarrow \dfrac{{{\left( 4x \right)}^{2}}}{{{\left( 3y \right)}^{2}}}\] …….. (1)
We know that 4 square gives 16 and 3 square gives 9 and if we square any variable, we can get the squared term of the variable, we can write the above step as,
\[\begin{align}
  & \Rightarrow {{\left( 4x \right)}^{2}}=16{{x}^{2}} \\
 & \Rightarrow {{\left( 3y \right)}^{2}}=9{{y}^{2}} \\
\end{align}\]
We can now substitute the above values in the step (1) for both the numerator and the denominator, we get
\[\Rightarrow \dfrac{{{\left( 4x \right)}^{2}}}{{{\left( 3y \right)}^{2}}}=\dfrac{16{{x}^{2}}}{9{{y}^{2}}}\]
Therefore, the simplified value of \[{{\left( \dfrac{4x}{3y} \right)}^{2}}\]is \[\dfrac{16{{x}^{2}}}{9{{y}^{2}}}\].

Note: Students make mistakes while squaring the terms, which should be concentrated. We also know how to square the numbers we should square each term using multiplication tables to get a simplified form. We know that 4 square gives 16 and 3 square gives 9 and if we square any variable, we can get the squared term of the variable.