Solve frac{4(x^{3}y^{5})^{3}div3(x^{2}y)^2}{(x^4y^2)^2}

$$\frac { 4 ( x ^ { 3 } y ^ { 5 } ) ^ { 3 } \div 3 ( x ^ { 2 } y ) ^ { 2 } } { ( x ^ { 4 } y ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{4x^{5}y^{13}}{3}$$

Solution Steps

Expand \left(x^{3}y^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{4x^{9}\left(y^{5}\right)^{3}}{3}\left(x^{2}y\right)^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\frac{4x^{9}y^{15}}{3}\left(x^{2}y\right)^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}}{3}\left(x^{2}\right)^{2}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}}{3}x^{4}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

Express \frac{4x^{9}y^{15}}{3}x^{4} as a single fraction.

$$\frac{\frac{4x^{9}y^{15}x^{4}}{3}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

Express \frac{4x^{9}y^{15}x^{4}}{3}y^{2} as a single fraction.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{\left(x^{4}y^{2}\right)^{2}}$$

Expand \left(x^{4}y^{2}\right)^{2}.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{\left(x^{4}\right)^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}\left(y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}y^{4}}$$

Express \frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}y^{4}} as a single fraction.

$$\frac{4x^{9}y^{15}x^{4}y^{2}}{3x^{8}y^{4}}$$

Cancel out y^{4}x^{8} in both numerator and denominator.

$$\frac{4xy^{2}x^{4}y^{11}}{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{4x^{5}y^{2}y^{11}}{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 11 to get 13.

$$\frac{4x^{5}y^{13}}{3}$$

Expand

$$\frac{4x^{5}y^{13}}{3}$$

Solution Steps

Expand \left(x^{3}y^{5}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\frac{4x^{9}\left(y^{5}\right)^{3}}{3}\left(x^{2}y\right)^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\frac{4x^{9}y^{15}}{3}\left(x^{2}y\right)^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}}{3}\left(x^{2}\right)^{2}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}}{3}x^{4}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

Express \frac{4x^{9}y^{15}}{3}x^{4} as a single fraction.

$$\frac{\frac{4x^{9}y^{15}x^{4}}{3}y^{2}}{\left(x^{4}y^{2}\right)^{2}}$$

Express \frac{4x^{9}y^{15}x^{4}}{3}y^{2} as a single fraction.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{\left(x^{4}y^{2}\right)^{2}}$$

Expand \left(x^{4}y^{2}\right)^{2}.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{\left(x^{4}\right)^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}\left(y^{2}\right)^{2}}$$

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

$$\frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}y^{4}}$$

Express \frac{\frac{4x^{9}y^{15}x^{4}y^{2}}{3}}{x^{8}y^{4}} as a single fraction.

$$\frac{4x^{9}y^{15}x^{4}y^{2}}{3x^{8}y^{4}}$$

Cancel out y^{4}x^{8} in both numerator and denominator.

$$\frac{4xy^{2}x^{4}y^{11}}{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{4x^{5}y^{2}y^{11}}{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 11 to get 13.

$$\frac{4x^{5}y^{13}}{3}$$