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

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

Evaluate

$$\frac{4x^{13}y^{17}}{3}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{4x^{13}y^{15}y^{2}}{3}$$

To multiply powers of the same base, add their exponents. Add 15 and 2 to get 17.

$$\frac{4x^{13}y^{17}}{3}$$

Expand

$$\frac{4x^{13}y^{17}}{3}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{4x^{13}y^{15}y^{2}}{3}$$

To multiply powers of the same base, add their exponents. Add 15 and 2 to get 17.

$$\frac{4x^{13}y^{17}}{3}$$