Solve frac{xy^{2}z^{3}}{3w^{3}y}*frac{wx^{2}}{(yz)^2}divx^3/6w^2y^3

$$\frac { x y ^ { 2 } z ^ { 3 } } { 3 w ^ { 3 } y } \times \frac { w x ^ { 2 } } { ( y z ) ^ { 2 } } \div \frac { x ^ { 3 } } { 6 w ^ { 2 } y ^ { 3 } }$$

Evaluate

$$2zy^{2}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{\frac{xyz^{3}}{3w^{3}}\times \frac{wx^{2}}{\left(yz\right)^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Expand \left(yz\right)^{2}.

$$\frac{\frac{xyz^{3}}{3w^{3}}\times \frac{wx^{2}}{y^{2}z^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Multiply \frac{xyz^{3}}{3w^{3}} times \frac{wx^{2}}{y^{2}z^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{xyz^{3}wx^{2}}{3w^{3}y^{2}z^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

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

$$\frac{\frac{xzx^{2}}{3yw^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Divide \frac{xzx^{2}}{3yw^{2}} by \frac{x^{3}}{6w^{2}y^{3}} by multiplying \frac{xzx^{2}}{3yw^{2}} by the reciprocal of \frac{x^{3}}{6w^{2}y^{3}}.

$$\frac{xzx^{2}\times 6w^{2}y^{3}}{3yw^{2}x^{3}}$$

Cancel out 3xyw^{2}x^{2} in both numerator and denominator.

$$2zy^{2}$$

Expand

$$2zy^{2}$$

Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{\frac{xyz^{3}}{3w^{3}}\times \frac{wx^{2}}{\left(yz\right)^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Expand \left(yz\right)^{2}.

$$\frac{\frac{xyz^{3}}{3w^{3}}\times \frac{wx^{2}}{y^{2}z^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Multiply \frac{xyz^{3}}{3w^{3}} times \frac{wx^{2}}{y^{2}z^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{xyz^{3}wx^{2}}{3w^{3}y^{2}z^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

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

$$\frac{\frac{xzx^{2}}{3yw^{2}}}{\frac{x^{3}}{6w^{2}y^{3}}}$$

Divide \frac{xzx^{2}}{3yw^{2}} by \frac{x^{3}}{6w^{2}y^{3}} by multiplying \frac{xzx^{2}}{3yw^{2}} by the reciprocal of \frac{x^{3}}{6w^{2}y^{3}}.

$$\frac{xzx^{2}\times 6w^{2}y^{3}}{3yw^{2}x^{3}}$$

Cancel out 3xyw^{2}x^{2} in both numerator and denominator.

$$2zy^{2}$$