Solve frac{12x^{3}y^2z}{5z^3}:6x^2y/10x^2z=

$$\frac { 12 x ^ { 3 } y ^ { 2 } z } { 5 z ^ { 3 } } : \frac { 6 x ^ { 2 } y } { 10 x ^ { 2 } z } =$$

Evaluate

$$\frac{4yx^{3}}{z}$$

Solution Steps

Divide \frac{12x^{3}y^{2}z}{5z^{3}} by \frac{6x^{2}y}{10x^{2}z} by multiplying \frac{12x^{3}y^{2}z}{5z^{3}} by the reciprocal of \frac{6x^{2}y}{10x^{2}z}.

$$\frac{12x^{3}y^{2}z\times 10x^{2}z}{5z^{3}\times 6x^{2}y}$$

Cancel out 5\times 6yzzx^{2} in both numerator and denominator.

$$\frac{2\times 2xyx^{2}}{z}$$

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

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

Multiply 2 and 2 to get 4.

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

Differentiate w.r.t. x

$$\frac{12yx^{2}}{z}$$