Solve 2/3xy^2*1/4x^3y^4*2/5x

$$\frac { 2 } { 3 } x y ^ { 2 } \times \frac { 1 } { 4 } x ^ { 3 } y ^ { 4 } \times \frac { 2 } { 5 } x$$

Evaluate

$$\frac{x^{5}y^{6}}{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{2}{3}x^{4}y^{2}\times \frac{1}{4}y^{4}\times \frac{2}{5}x$$

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

$$\frac{2}{3}x^{5}y^{2}\times \frac{1}{4}y^{4}\times \frac{2}{5}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{2}{3}x^{5}y^{6}\times \frac{1}{4}\times \frac{2}{5}$$

Multiply \frac{2}{3} and \frac{1}{4} to get \frac{1}{6}.

$$\frac{1}{6}x^{5}y^{6}\times \frac{2}{5}$$

Multiply \frac{1}{6} and \frac{2}{5} to get \frac{1}{15}.

$$\frac{1}{15}x^{5}y^{6}$$

Differentiate w.r.t. x

$$\frac{x^{4}y^{6}}{3}$$