Solve (2xy^2)^2(3xy)^3=

$$( 2 x y ^ { 2 } ) ^ { 2 } ( 3 x y ) ^ { 3 } =$$

Evaluate

$$108x^{5}y^{7}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 3 and get 27.

$$4x^{2}y^{4}\times 27x^{3}y^{3}$$

Multiply 4 and 27 to get 108.

$$108x^{2}y^{4}x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$108x^{5}y^{4}y^{3}$$

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

$$108x^{5}y^{7}$$

Expand

$$108x^{5}y^{7}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 3 and get 27.

$$4x^{2}y^{4}\times 27x^{3}y^{3}$$

Multiply 4 and 27 to get 108.

$$108x^{2}y^{4}x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$108x^{5}y^{4}y^{3}$$

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

$$108x^{5}y^{7}$$