Solve (2xy^2)^3x(3xy)^2

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

Evaluate

$$72x^{6}y^{8}$$

Solution Steps

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

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

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

$$2^{3}x^{3}y^{6}x\times \left(3xy\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{3}y^{6}x\times \left(3xy\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$8x^{4}y^{6}\times \left(3xy\right)^{2}$$

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

$$8x^{4}y^{6}\times 3^{2}x^{2}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$8x^{4}y^{6}\times 9x^{2}y^{2}$$

Multiply 8 and 9 to get 72.

$$72x^{4}y^{6}x^{2}y^{2}$$

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

$$72x^{6}y^{6}y^{2}$$

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

$$72x^{6}y^{8}$$

Expand

$$72x^{6}y^{8}$$

Solution Steps

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

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

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

$$2^{3}x^{3}y^{6}x\times \left(3xy\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{3}y^{6}x\times \left(3xy\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$8x^{4}y^{6}\times \left(3xy\right)^{2}$$

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

$$8x^{4}y^{6}\times 3^{2}x^{2}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$8x^{4}y^{6}\times 9x^{2}y^{2}$$

Multiply 8 and 9 to get 72.

$$72x^{4}y^{6}x^{2}y^{2}$$

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

$$72x^{6}y^{6}y^{2}$$

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

$$72x^{6}y^{8}$$