Solve (-2x^2y^3)^2*(xy)^2

$$( - 2 x ^ { 2 } y ^ { 3 } ) ^ { 2 } \cdot ( x y ) ^ { 2 }$$

Evaluate

$$4x^{6}y^{8}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

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

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

$$4x^{4}y^{6}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$4x^{6}y^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$4x^{6}y^{8}$$

Expand

$$4x^{6}y^{8}$$

Solution Steps

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

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

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

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

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

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

Calculate -2 to the power of 2 and get 4.

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

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

$$4x^{4}y^{6}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$4x^{6}y^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$4x^{6}y^{8}$$