Solve frac{20x^{4}}{5xy^2}div15x^2y^3/12y^2

$$\frac { 20 x ^ { 4 } } { 5 x y ^ { 2 } } \div \frac { 15 x ^ { 2 } y ^ { 3 } } { 12 y ^ { 2 } }$$

Evaluate

$$\frac{16x}{5y^{3}}$$

Solution Steps

Divide \frac{20x^{4}}{5xy^{2}} by \frac{15x^{2}y^{3}}{12y^{2}} by multiplying \frac{20x^{4}}{5xy^{2}} by the reciprocal of \frac{15x^{2}y^{3}}{12y^{2}}.

$$\frac{20x^{4}\times 12y^{2}}{5xy^{2}\times 15x^{2}y^{3}}$$

Cancel out 3\times 5xx^{2}y^{2} in both numerator and denominator.

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

Multiply 4 and 4 to get 16.

$$\frac{16x}{5y^{3}}$$

Differentiate w.r.t. x

$$\frac{16}{5y^{3}}$$