Solve (xy^{2})^{3}(x^{2}y)^{2}+(x^{3}y^4)(x^2y^2)^2

$$( x y ^ { 2 } ) ^ { 3 } ( x ^ { 2 } y ) ^ { 2 } + ( x ^ { 3 } y ^ { 4 } ) ( x ^ { 2 } y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$2x^{7}y^{8}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}y^{6}y^{2}+x^{3}y^{4}\left(x^{2}y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}\left(x^{2}y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}x^{4}\left(y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}y^{8}+x^{7}y^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$x^{7}y^{8}+x^{7}y^{8}$$

Combine x^{7}y^{8} and x^{7}y^{8} to get 2x^{7}y^{8}.

$$2x^{7}y^{8}$$

Expand

$$2x^{7}y^{8}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}y^{6}y^{2}+x^{3}y^{4}\left(x^{2}y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}\left(x^{2}y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}x^{4}\left(y^{2}\right)^{2}$$

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

$$x^{7}y^{8}+x^{3}y^{4}x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}y^{8}+x^{7}y^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$x^{7}y^{8}+x^{7}y^{8}$$

Combine x^{7}y^{8} and x^{7}y^{8} to get 2x^{7}y^{8}.

$$2x^{7}y^{8}$$