Solve (6x^2y^3)^2div(2xy)^3

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

Evaluate

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

Solution Steps

Expand \left(6x^{2}y^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{\left(2xy\right)^{3}}$$

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

$$\frac{6^{2}x^{4}\left(y^{3}\right)^{2}}{\left(2xy\right)^{3}}$$

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

$$\frac{6^{2}x^{4}y^{6}}{\left(2xy\right)^{3}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{4}y^{6}}{\left(2xy\right)^{3}}$$

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

$$\frac{36x^{4}y^{6}}{2^{3}x^{3}y^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{36x^{4}y^{6}}{8x^{3}y^{3}}$$

Cancel out 4x^{3}y^{3} in both numerator and denominator.

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

Expand

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

Solution Steps

Expand \left(6x^{2}y^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{\left(2xy\right)^{3}}$$

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

$$\frac{6^{2}x^{4}\left(y^{3}\right)^{2}}{\left(2xy\right)^{3}}$$

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

$$\frac{6^{2}x^{4}y^{6}}{\left(2xy\right)^{3}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{4}y^{6}}{\left(2xy\right)^{3}}$$

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

$$\frac{36x^{4}y^{6}}{2^{3}x^{3}y^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{36x^{4}y^{6}}{8x^{3}y^{3}}$$

Cancel out 4x^{3}y^{3} in both numerator and denominator.

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