Solve 273x^4/5y:2x/15y^3=

$$27 \frac { 3 x ^ { 4 } } { 5 y } : \frac { 2 x } { 15 y ^ { 3 } } =$$

Evaluate

$$\frac{243y^{2}x^{3}}{2}$$

Solution Steps

Express 27\times \frac{3x^{4}}{5y} as a single fraction.

$$\frac{\frac{27\times 3x^{4}}{5y}}{\frac{2x}{15y^{3}}}$$

Divide \frac{27\times 3x^{4}}{5y} by \frac{2x}{15y^{3}} by multiplying \frac{27\times 3x^{4}}{5y} by the reciprocal of \frac{2x}{15y^{3}}.

$$\frac{27\times 3x^{4}\times 15y^{3}}{5y\times 2x}$$

Cancel out 5xy in both numerator and denominator.

$$\frac{3\times 3\times 27y^{2}x^{3}}{2}$$

Multiply 3 and 3 to get 9.

$$\frac{9\times 27y^{2}x^{3}}{2}$$

Multiply 9 and 27 to get 243.

$$\frac{243y^{2}x^{3}}{2}$$

Differentiate w.r.t. x

$$\frac{729\left(xy\right)^{2}}{2}$$