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

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

Evaluate

$$4y^{5}$$

Solution Steps

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

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

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

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

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

$$4x^{2}y^{6}\left(x^{2}y\right)^{-1}$$

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

$$4x^{2}y^{6}\left(x^{2}\right)^{-1}y^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$4x^{2}y^{6}x^{-2}y^{-1}$$

Multiply x^{2} and x^{-2} to get 1.

$$4y^{6}y^{-1}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$4y^{5}$$

Expand

$$4y^{5}$$

Solution Steps

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

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

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

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

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

$$4x^{2}y^{6}\left(x^{2}y\right)^{-1}$$

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

$$4x^{2}y^{6}\left(x^{2}\right)^{-1}y^{-1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$4x^{2}y^{6}x^{-2}y^{-1}$$

Multiply x^{2} and x^{-2} to get 1.

$$4y^{6}y^{-1}$$

To multiply powers of the same base, add their exponents. Add 6 and -1 to get 5.

$$4y^{5}$$