Solve (3x^{2}y)^2(2x^4y^2)^2?

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

Evaluate

$$36y^{6}x^{12}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{2}\times \left(2x^{4}y^{2}\right)^{2}$$

Expand \left(2x^{4}y^{2}\right)^{2}.

$$9x^{4}y^{2}\times 2^{2}\left(x^{4}\right)^{2}\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$9x^{4}y^{2}\times 2^{2}x^{8}\left(y^{2}\right)^{2}$$

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

$$9x^{4}y^{2}\times 2^{2}x^{8}y^{4}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{4}y^{2}\times 4x^{8}y^{4}$$

Multiply 9 and 4 to get 36.

$$36x^{4}y^{2}x^{8}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$36x^{12}y^{2}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$36x^{12}y^{6}$$

Expand

$$36y^{6}x^{12}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{2}\times \left(2x^{4}y^{2}\right)^{2}$$

Expand \left(2x^{4}y^{2}\right)^{2}.

$$9x^{4}y^{2}\times 2^{2}\left(x^{4}\right)^{2}\left(y^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$9x^{4}y^{2}\times 2^{2}x^{8}\left(y^{2}\right)^{2}$$

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

$$9x^{4}y^{2}\times 2^{2}x^{8}y^{4}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{4}y^{2}\times 4x^{8}y^{4}$$

Multiply 9 and 4 to get 36.

$$36x^{4}y^{2}x^{8}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$36x^{12}y^{2}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$36x^{12}y^{6}$$