The simplified expression is [tex]-\frac{48}{x^{3} y^{3}}[/tex]
Explanation:
The given expression is [tex]\frac{-12x^{2}12y^{2} }{3x^{5} y^{5} }[/tex]
Let us simplify the expression.
Multiplying the numbers in the numerator, we have,
[tex]\frac{-144 x^{2} y^{2}}{3 x^{5} y^{5}}[/tex]
Dividing the term 144 by 3, which results in 48.
Thus, we have,
[tex]\frac{-48 x^{2} y^{2}}{x^{5} y^{5}}[/tex]
Applying the fraction rule [tex]\frac{-a}{b}=-\frac{a}{b}[/tex] , we get,
[tex]-\frac{48 x^{2} y^{2}}{x^{5} y^{5}}[/tex]
Applying the exponent rule [tex]\frac{x^{a}}{x^{b}}=\frac{1}{x^{b-a}}[/tex], we have,
[tex]-\frac{48}{x^{3} y^{3}}[/tex]
Thus, the simplified expression is [tex]-\frac{48}{x^{3} y^{3}}[/tex]
