Solve 2xy^4div9xy*1/9y^2

$$2 x y ^ { 4 } \div 9 x y \cdot \frac { 1 } { 9 } y ^ { 2 }$$

Evaluate

$$\frac{2x^{2}y^{7}}{81}$$

Solution Steps

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

$$\frac{2xy^{4}}{9}xy^{3}\times \frac{1}{9}$$

Express \frac{2xy^{4}}{9}x as a single fraction.

$$\frac{2xy^{4}x}{9}y^{3}\times \frac{1}{9}$$

Express \frac{2xy^{4}x}{9}y^{3} as a single fraction.

$$\frac{2xy^{4}xy^{3}}{9}\times \frac{1}{9}$$

Multiply \frac{2xy^{4}xy^{3}}{9} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2xy^{4}xy^{3}}{9\times 9}$$

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

$$\frac{2x^{2}y^{4}y^{3}}{9\times 9}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{2x^{2}y^{7}}{9\times 9}$$

Multiply 9 and 9 to get 81.

$$\frac{2x^{2}y^{7}}{81}$$

Differentiate w.r.t. x

$$\frac{4xy^{7}}{81}$$