Solve (frac{5n^{3}}{3x^{2}y^3})(3x^2y^-1/2x^3)

$$( \frac { 5 n ^ { 3 } } { 3 x ^ { 2 } y ^ { 3 } } ) ( \frac { 3 x ^ { 2 } y ^ { - 1 } } { 2 x ^ { 3 } } )$$

Evaluate

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

Solution Steps

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

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

Express 3\times \frac{1}{y} as a single fraction.

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

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

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

Multiply \frac{5n^{3}}{3x^{2}y^{3}} times \frac{3}{y\times 2x} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{5n^{3}}{2xyx^{2}y^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{5n^{3}}{2x^{3}yy^{3}}$$

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

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

Differentiate w.r.t. x

$$-\frac{15n^{3}}{2\left(xy\right)^{4}}$$