Solve (x^{4}y)(frac{3x^{4}y^-3z}{6x^3y^2z^4})

$$( x ^ { 4 } y ) ( \frac { 3 x ^ { 4 } y ^ { - 3 } z } { 6 x ^ { 3 } y ^ { 2 } z ^ { 4 } } )$$

Evaluate

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

Solution Steps

Cancel out 3zx^{3} in both numerator and denominator.

$$x^{4}y\times \frac{y^{-3}x}{2y^{2}z^{3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Express x^{4}\times \frac{x}{2z^{3}y^{5}} as a single fraction.

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

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

$$\frac{x^{5}}{2z^{3}y^{5}}y$$

Express \frac{x^{5}}{2z^{3}y^{5}}y as a single fraction.

$$\frac{x^{5}y}{2z^{3}y^{5}}$$

Cancel out y in both numerator and denominator.

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

Differentiate w.r.t. x

$$\frac{5\times \left(\frac{x}{y}\right)^{4}}{2z^{3}}$$