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$\frac{\left(x^{-\frac{1}{5}}\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule ((x^(-1/5)y^(3/2))^10)/((y^((1*-2)/5)x^2/3)^5). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. . Simplify \left(y^{-\frac{2}{5}}\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals -\frac{2}{5} and n equals 5.