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

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

Evaluate

$$72y^{8}x^{13}$$

Solution Steps

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

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

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

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

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

$$2^{3}x^{9}y^{6}\times \left(3x^{2}y\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{9}y^{6}\times \left(3x^{2}y\right)^{2}$$

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

$$8x^{9}y^{6}\times 3^{2}\left(x^{2}\right)^{2}y^{2}$$

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

$$8x^{9}y^{6}\times 3^{2}x^{4}y^{2}$$

Calculate 3 to the power of 2 and get 9.

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

Multiply 8 and 9 to get 72.

$$72x^{9}y^{6}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$72x^{13}y^{6}y^{2}$$

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

$$72x^{13}y^{8}$$

Expand

$$72y^{8}x^{13}$$

Solution Steps

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

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

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

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

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

$$2^{3}x^{9}y^{6}\times \left(3x^{2}y\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{9}y^{6}\times \left(3x^{2}y\right)^{2}$$

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

$$8x^{9}y^{6}\times 3^{2}\left(x^{2}\right)^{2}y^{2}$$

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

$$8x^{9}y^{6}\times 3^{2}x^{4}y^{2}$$

Calculate 3 to the power of 2 and get 9.

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

Multiply 8 and 9 to get 72.

$$72x^{9}y^{6}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$72x^{13}y^{6}y^{2}$$

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

$$72x^{13}y^{8}$$