Solve 2/3xy^2div1/4x^3y^4*2/5x

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

Evaluate

$$\frac{16x^{5}y^{6}}{15}$$

Solution Steps

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

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

Divide \frac{2}{3}xy^{2} by \frac{1}{4} by multiplying \frac{2}{3}xy^{2} by the reciprocal of \frac{1}{4}.

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

Multiply \frac{2}{3} and 4 to get \frac{8}{3}.

$$\frac{8}{3}xy^{2}x^{4}y^{4}\times \frac{2}{5}$$

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

$$\frac{8}{3}x^{5}y^{2}y^{4}\times \frac{2}{5}$$

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

$$\frac{8}{3}x^{5}y^{6}\times \frac{2}{5}$$

Multiply \frac{8}{3} and \frac{2}{5} to get \frac{16}{15}.

$$\frac{16}{15}x^{5}y^{6}$$

Differentiate w.r.t. x

$$\frac{16x^{4}y^{6}}{3}$$