Solve 4x^2ydivxy/(2x)^2*16x^2y/(2xy)^2

$$4 x ^ { 2 } y \div \frac { x y } { ( 2 x ) ^ { 2 } } \times \frac { 16 x ^ { 2 } y } { ( 2 x y ) ^ { 2 } }$$

Evaluate

$$\frac{64x^{3}}{y}$$

Solution Steps

Divide 4x^{2}y by \frac{xy}{\left(2x\right)^{2}} by multiplying 4x^{2}y by the reciprocal of \frac{xy}{\left(2x\right)^{2}}.

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

Cancel out xy in both numerator and denominator.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$16xx^{2}\times \frac{16x^{2}y}{\left(2xy\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

$$16x^{3}\times \frac{16x^{2}y}{2^{2}x^{2}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

Cancel out 4yx^{2} in both numerator and denominator.

$$16x^{3}\times \frac{4}{y}$$

Express 16\times \frac{4}{y} as a single fraction.

$$\frac{16\times 4}{y}x^{3}$$

Multiply 16 and 4 to get 64.

$$\frac{64}{y}x^{3}$$

Express \frac{64}{y}x^{3} as a single fraction.

$$\frac{64x^{3}}{y}$$

Expand

$$\frac{64x^{3}}{y}$$

Solution Steps

Divide 4x^{2}y by \frac{xy}{\left(2x\right)^{2}} by multiplying 4x^{2}y by the reciprocal of \frac{xy}{\left(2x\right)^{2}}.

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

Cancel out xy in both numerator and denominator.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$16xx^{2}\times \frac{16x^{2}y}{\left(2xy\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

$$16x^{3}\times \frac{16x^{2}y}{2^{2}x^{2}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

Cancel out 4yx^{2} in both numerator and denominator.

$$16x^{3}\times \frac{4}{y}$$

Express 16\times \frac{4}{y} as a single fraction.

$$\frac{16\times 4}{y}x^{3}$$

Multiply 16 and 4 to get 64.

$$\frac{64}{y}x^{3}$$

Express \frac{64}{y}x^{3} as a single fraction.

$$\frac{64x^{3}}{y}$$