Solve (-y^2*-xy^-1)^3

$$( - y ^ { 2 } \cdot - x y ^ { - 1 } ) ^ { 3 }$$

Evaluate

$$\left(xy\right)^{3}$$

Solution Steps

Expand \left(\left(-y^{2}\right)\left(-x\right)y^{-1}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$y^{6}x^{3}y^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$y^{3}x^{3}$$

Expand

$$\left(xy\right)^{3}$$

Solution Steps

Expand \left(\left(-y^{2}\right)\left(-x\right)y^{-1}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

$$y^{6}x^{3}y^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -3 to get 3.

$$y^{3}x^{3}$$