Solve (xy^{2}[x^3y^2]^3)^2

$$( x y ^ { 2 } [ x ^ { 3 } y ^ { 2 } ] ^ { 3 } ) ^ { 2 }$$

Evaluate

$$y^{16}x^{20}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(xy^{2}x^{9}\left(y^{2}\right)^{3}\right)^{2}$$

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

$$\left(xy^{2}x^{9}y^{6}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\left(x^{10}y^{2}y^{6}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\left(x^{10}y^{8}\right)^{2}$$

Expand \left(x^{10}y^{8}\right)^{2}.

$$\left(x^{10}\right)^{2}\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$x^{20}\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$x^{20}y^{16}$$

Expand

$$y^{16}x^{20}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(xy^{2}x^{9}\left(y^{2}\right)^{3}\right)^{2}$$

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

$$\left(xy^{2}x^{9}y^{6}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\left(x^{10}y^{2}y^{6}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\left(x^{10}y^{8}\right)^{2}$$

Expand \left(x^{10}y^{8}\right)^{2}.

$$\left(x^{10}\right)^{2}\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$x^{20}\left(y^{8}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$x^{20}y^{16}$$