Solve x^{2}y*(x^3)^4*(y^2)^2

$$x ^ { 2 } y \times ( x ^ { 3 } ) ^ { 4 } \times ( y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$y^{5}x^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$x^{2}yx^{12}\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{2}yx^{12}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$x^{14}yy^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$x^{14}y^{5}$$

Differentiate w.r.t. x

$$14y^{5}x^{13}$$