Solve frac{(x^{2}y^{3})^{2}+(x^{3}y^2)(x^2y^3)}{xy+y^2}

$$\frac { ( x ^ { 2 } y ^ { 3 } ) ^ { 2 } + ( x ^ { 3 } y ^ { 2 } ) ( x ^ { 2 } y ^ { 3 } ) } { x y + y ^ { 2 } }$$

Evaluate

$$\left(xy\right)^{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(x^{2}y^{3}\right)^{2}+x^{5}y^{2}y^{3}}{xy+y^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(x^{2}y^{3}\right)^{2}+x^{5}y^{5}}{xy+y^{2}}$$

Expand \left(x^{2}y^{3}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}+x^{5}y^{5}}{xy+y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{x^{4}y^{6}+x^{5}y^{5}}{xy+y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+y\right)x^{4}y^{5}}{y\left(x+y\right)}$$

Cancel out y\left(x+y\right) in both numerator and denominator.

$$x^{4}y^{4}$$

Expand

$$\left(xy\right)^{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\left(x^{2}y^{3}\right)^{2}+x^{5}y^{2}y^{3}}{xy+y^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\left(x^{2}y^{3}\right)^{2}+x^{5}y^{5}}{xy+y^{2}}$$

Expand \left(x^{2}y^{3}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}+x^{5}y^{5}}{xy+y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{x^{4}y^{6}+x^{5}y^{5}}{xy+y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+y\right)x^{4}y^{5}}{y\left(x+y\right)}$$

Cancel out y\left(x+y\right) in both numerator and denominator.

$$x^{4}y^{4}$$