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# How do you simplify the expression ${\left( {3{x^2}{y^3}} \right)^{ - 2}}$ ?

Last updated date: 09th Aug 2024
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Hint:In the given question, we are required to find the value of inverse of the square of the expression $\left( {3{x^2}{y^3}} \right)$. Given is a bracket with an expression involving two variables, x and y. So, we have to evaluate the inverse of the square of the term. Square is nothing but multiplying the same number with itself. So we will multiply the bracket with itself. Then each individual term in the first bracket is multiplied with that in the second term. Then if needed any mathematical operations, those will be performed. Or else we can use the standard and important identities used for expansion. Like those used in squaring or cubing. Those are the algebraic identities that come in significant use when solving such questions.
Given that: ${\left( {3{x^2}{y^3}} \right)^{ - 2}}$. So, we have to find the inverse of the square of the expression $\left( {3{x^2}{y^3}} \right)$.
${\left( {3{x^2}{y^3}} \right)^2} = \left( {9{x^4}{y^6}} \right)$
Now, we have to find the inverse of the obtained expression to get the required final result.Inverse of an expression is reciprocal of the expression.So, Inverse of $\left( {9{x^4}{y^6}} \right)$ is $\dfrac{1}{{9{x^4}{y^6}}}$.
So, the expression ${\left( {3{x^2}{y^3}} \right)^{ - 2}}$ given to us can be simplified as $\dfrac{1}{{9{x^4}{y^6}}}$.