Solve (2x^2y^-1)^2(4xy^3)

$$( 2 x ^ { 2 } y ^ { - 1 } ) ^ { 2 } ( 4 x y ^ { 3 } )$$

Evaluate

$$16yx^{5}$$

Solution Steps

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

$$2^{2}\left(x^{2}\right)^{2}\left(y^{-1}\right)^{2}\times 4xy^{3}$$

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

$$2^{2}x^{4}\left(y^{-1}\right)^{2}\times 4xy^{3}$$

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$16x^{4}y^{-2}xy^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$16x^{5}y^{-2}y^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$16x^{5}y^{1}$$

Calculate y to the power of 1 and get y.

$$16x^{5}y$$

Expand

$$16yx^{5}$$

Solution Steps

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

$$2^{2}\left(x^{2}\right)^{2}\left(y^{-1}\right)^{2}\times 4xy^{3}$$

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

$$2^{2}x^{4}\left(y^{-1}\right)^{2}\times 4xy^{3}$$

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 4 to get 16.

$$16x^{4}y^{-2}xy^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$16x^{5}y^{-2}y^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$16x^{5}y^{1}$$

Calculate y to the power of 1 and get y.

$$16x^{5}y$$