Solve 1/3y^2zdiv5/9yz

$$\frac { 1 } { 3 } y ^ { 2 } z \div \frac { 5 } { 9 } y z$$

Evaluate

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

Solution Steps

Divide \frac{1}{3}y^{2}z by \frac{5}{9} by multiplying \frac{1}{3}y^{2}z by the reciprocal of \frac{5}{9}.

$$\frac{\frac{1}{3}y^{2}z\times 9}{5}yz$$

Multiply \frac{1}{3} and 9 to get 3.

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

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

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

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

$$\frac{3y^{2}zyz}{5}$$

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

$$\frac{3y^{3}zz}{5}$$

Multiply z and z to get z^{2}.

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

Differentiate w.r.t. y

$$\frac{9\left(yz\right)^{2}}{5}$$