Question

d. \\(\dfrac{(x^{4}y^{2})^{3}}{(x^{2}y^{2})^{2}}\\)

Explanation:

Step1: Apply power of a product rule

For numerator: $(x^4y^2)^3 = x^{4\times3}y^{2\times3} = x^{12}y^6$
For denominator: $(x^2y^2)^2 = x^{2\times2}y^{2\times2} = x^4y^4$
The expression becomes $\frac{x^{12}y^6}{x^4y^4}$

Step2: Apply quotient of powers rule

For $x$-terms: $x^{12-4}=x^8$
For $y$-terms: $y^{6-4}=y^2$
Combine results: $x^8y^2$

Answer:

$x^8y^2$