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

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

Evaluate

$$y^{4}$$

Solution Steps

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

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

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

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

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

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

Calculate -x^{-3} to the power of 2 and get \left(x^{-3}\right)^{2}.

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

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

$$x^{6}y^{4}\left(x^{-3}\right)^{2}$$

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

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

Multiply x^{6} and x^{-6} to get 1.

$$y^{4}$$

Expand

$$y^{4}$$

Solution Steps

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

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

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

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

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

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

Calculate -x^{-3} to the power of 2 and get \left(x^{-3}\right)^{2}.

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

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

$$x^{6}y^{4}\left(x^{-3}\right)^{2}$$

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

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

Multiply x^{6} and x^{-6} to get 1.

$$y^{4}$$