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

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

Evaluate

$$-72x^{7}y^{8}$$

Solution Steps

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

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

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

$$\left(-2\right)^{3}x^{3}y^{6}\times \left(3x^{2}y\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{3}y^{6}\times \left(3x^{2}y\right)^{2}$$

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

$$-8x^{3}y^{6}\times 3^{2}\left(x^{2}\right)^{2}y^{2}$$

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

$$-8x^{3}y^{6}\times 3^{2}x^{4}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-8x^{3}y^{6}\times 9x^{4}y^{2}$$

Multiply -8 and 9 to get -72.

$$-72x^{3}y^{6}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-72x^{7}y^{6}y^{2}$$

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

$$-72x^{7}y^{8}$$

Expand

$$-72x^{7}y^{8}$$

Solution Steps

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

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

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

$$\left(-2\right)^{3}x^{3}y^{6}\times \left(3x^{2}y\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{3}y^{6}\times \left(3x^{2}y\right)^{2}$$

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

$$-8x^{3}y^{6}\times 3^{2}\left(x^{2}\right)^{2}y^{2}$$

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

$$-8x^{3}y^{6}\times 3^{2}x^{4}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-8x^{3}y^{6}\times 9x^{4}y^{2}$$

Multiply -8 and 9 to get -72.

$$-72x^{3}y^{6}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-72x^{7}y^{6}y^{2}$$

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

$$-72x^{7}y^{8}$$