Solve frac{6x^{4}b^{3}}{5a^2y^4}:(-5xb^2/9a^2y)

$$\frac { 6 x ^ { 4 } b ^ { 3 } } { 5 a ^ { 2 } y ^ { 4 } } : ( - \frac { 5 x b ^ { 2 } } { 9 a ^ { 2 } y } )$$

Evaluate

$$-\frac{54\times \left(\frac{x}{y}\right)^{3}b}{25}$$

Solution Steps

Express \frac{\frac{6x^{4}b^{3}}{5a^{2}y^{4}}}{-\frac{5xb^{2}}{9a^{2}y}} as a single fraction.

$$\frac{6x^{4}b^{3}}{5a^{2}y^{4}\left(-\frac{5xb^{2}}{9a^{2}y}\right)}$$

Express 5\left(-\frac{5xb^{2}}{9a^{2}y}\right) as a single fraction.

$$\frac{6x^{4}b^{3}}{\frac{-5\times 5xb^{2}}{9a^{2}y}a^{2}y^{4}}$$

Multiply -5 and 5 to get -25.

$$\frac{6x^{4}b^{3}}{\frac{-25xb^{2}}{9a^{2}y}a^{2}y^{4}}$$

Express \frac{-25xb^{2}}{9a^{2}y}a^{2} as a single fraction.

$$\frac{6x^{4}b^{3}}{\frac{-25xb^{2}a^{2}}{9a^{2}y}y^{4}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{6x^{4}b^{3}}{\frac{-25xb^{2}}{9y}y^{4}}$$

Express \frac{-25xb^{2}}{9y}y^{4} as a single fraction.

$$\frac{6x^{4}b^{3}}{\frac{-25xb^{2}y^{4}}{9y}}$$

Cancel out y in both numerator and denominator.

$$\frac{6x^{4}b^{3}}{\frac{-25xb^{2}y^{3}}{9}}$$

Divide 6x^{4}b^{3} by \frac{-25xb^{2}y^{3}}{9} by multiplying 6x^{4}b^{3} by the reciprocal of \frac{-25xb^{2}y^{3}}{9}.

$$\frac{6x^{4}b^{3}\times 9}{-25xb^{2}y^{3}}$$

Cancel out xb^{2} in both numerator and denominator.

$$\frac{6\times 9bx^{3}}{-25y^{3}}$$

Multiply 6 and 9 to get 54.

$$\frac{54bx^{3}}{-25y^{3}}$$

Differentiate w.r.t. x

$$-\frac{162bx^{2}}{25y^{3}}$$