Solve (4x^2y^3)^2/(2xy)^3

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

Evaluate

$$2xy^{3}$$

Solution Steps

Expand \left(4x^{2}y^{3}\right)^{2}.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{4}y^{6}}{\left(2xy\right)^{3}}$$

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

$$\frac{16x^{4}y^{6}}{2^{3}x^{3}y^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{16x^{4}y^{6}}{8x^{3}y^{3}}$$

Cancel out 8x^{3}y^{3} in both numerator and denominator.

$$2xy^{3}$$

Expand

$$2xy^{3}$$

Solution Steps

Expand \left(4x^{2}y^{3}\right)^{2}.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{4}y^{6}}{\left(2xy\right)^{3}}$$

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

$$\frac{16x^{4}y^{6}}{2^{3}x^{3}y^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{16x^{4}y^{6}}{8x^{3}y^{3}}$$

Cancel out 8x^{3}y^{3} in both numerator and denominator.

$$2xy^{3}$$