Solve (x^3y)^3*(2xy)^2*6y/3x^2y

$$\frac { ( x ^ { 3 } y ) ^ { 3 } \times ( 2 x y ) ^ { 2 } \times 6 y } { 3 x ^ { 2 } y }$$

Evaluate

$$8y^{5}x^{9}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

$$\frac{2\times \left(2xy\right)^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Expand \left(2xy\right)^{2}.

$$\frac{2\times 2^{2}x^{2}y^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

Multiply 2 and 4 to get 8.

$$\frac{8x^{2}y^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Expand \left(yx^{3}\right)^{3}.

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

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

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

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

$$\frac{8x^{2}y^{5}x^{9}}{x^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\frac{8x^{11}y^{5}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$8y^{5}x^{9}$$

Expand

$$8y^{5}x^{9}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

$$\frac{2\times \left(2xy\right)^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Expand \left(2xy\right)^{2}.

$$\frac{2\times 2^{2}x^{2}y^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

Multiply 2 and 4 to get 8.

$$\frac{8x^{2}y^{2}\left(yx^{3}\right)^{3}}{x^{2}}$$

Expand \left(yx^{3}\right)^{3}.

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

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

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

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

$$\frac{8x^{2}y^{5}x^{9}}{x^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\frac{8x^{11}y^{5}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$8y^{5}x^{9}$$