How do you simplify \[{\left( {\dfrac{{3x{y^4}}}{{5{z^2}}}} \right)^2}\] ?

Hint: We have given an algebraic expression and we have to simplify the given expression. To simplify the given expression, we use the power rule of exponent

Complete step by step answer:
Step 1: Given expression is \[{\left( {\dfrac{{3x{y^4}}}{{5{z^2}}}} \right)^2}\]
First we rewrite the given expression as
\[ \Rightarrow {\left( {\dfrac{{{3^1}{x^1}{y^4}}}{{{5^1}{z^2}}}} \right)^2}\]
Step 2: Now we use the power rule of exponent to eliminate the exponent outside the parentheses, we get
\[ \Rightarrow \left( {\dfrac{{{3^{1 \times 2}}{x^{1 \times 2}}{y^{4 \times 2}}}}{{{5^{1 \times 2}}{z^{2 \times 2}}}}} \right)\]
Step 3: Simplifying the above expression, we get
\[ \Rightarrow \left( {\dfrac{{{3^2}{x^2}{y^8}}}{{{5^2}{z^4}}}} \right)\]
Step 4: Now we know that ${3^2} = 9$ and ${5^2} = 25$ . Substituting the values, we get
\[ \Rightarrow \dfrac{{9{x^2}{y^8}}}{{25{z^4}}}\]
This is the simplified expression.

Note: The value of any constant or variable power to zero is always $1$ , which means ${\left( c \right)^0} = 1$ where $c$ is any constant or any variable.
The value of any constant or variable power to one is the same constant or variable, which means ${\left( x \right)^1} = x$ , where $x$ is any constant or variable.