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

Hint: To simplify this question , we need to solve it step by step . We will cancel out the like terms in the numerator and the denominator for simplification . . We should know that the exponents having -1 as power is considered to be $ $ $ \dfrac{1}{x} $ . So , by rewriting all the powers having negative exponents can be rewritten by using only positive exponents . Also make the group of like variables together . Here we have two variables having negative exponents , we will rewrite it similarly and try to simplify by cancelling out the common factors to get the required result .

Complete step-by-step answer:
In order to solve the expression , write it the way it is given and then arrange it –
 $ {\left( {\dfrac{{2{x^{ - 5}}{y^2}}}{{4{x^3}{y^{ - 4}}}}} \right)^{ - 3}} $
Now apply the formula of $ = \dfrac{1}{x} = {x^{ - 1}} $
Now we can use the formula of solving the exponents \[{a^m} \cdot {a^n} = {a^{m + n}}\]
Now you can separate the exponents within individual terms =
Therefore , the solution to this question is $ \dfrac{{8{x^{24}}}}{{{y^{ - 18}}}} $ .
So, the correct answer is “ $ \dfrac{{8{x^{24}}}}{{{y^{ - 18}}}} $ ”.

Note: Always remember you can perform calculations only between like terms .
The expression is having hidden multiplication when written altogether .
Make sure the calculation in the question is done correctly.
To calculate the simplified answer try to break out the steps from the question.
Always check the required formula exponent rule and try to cancel out the common factors.
If the base of the exponent number is prime, we cannot simplify the question further and answer is obtained by simply calculating the exponent value.
Do not forget to verify the exponents solved correctly .
Always try to cancel out the similar terms for the solution of simplification .