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

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

Evaluate

$$-2y^{5}x^{7}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-x^{2}\right)^{3}y^{5}\times 2x$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{5}\times 2x$$

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

$$\left(-1\right)^{3}x^{6}y^{5}\times 2x$$

Calculate -1 to the power of 3 and get -1.

$$-x^{6}y^{5}\times 2x$$

Multiply -1 and 2 to get -2.

$$-2x^{6}y^{5}x$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-2x^{7}y^{5}$$

Expand

$$-2y^{5}x^{7}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-x^{2}\right)^{3}y^{5}\times 2x$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{5}\times 2x$$

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

$$\left(-1\right)^{3}x^{6}y^{5}\times 2x$$

Calculate -1 to the power of 3 and get -1.

$$-x^{6}y^{5}\times 2x$$

Multiply -1 and 2 to get -2.

$$-2x^{6}y^{5}x$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-2x^{7}y^{5}$$