Solve (3xy)^3(4x^3y^5)^2

$$( 3 x y ) ^ { 3 } ( 4 x ^ { 3 } y ^ { 5 } ) ^ { 2 }$$

Evaluate

$$432x^{9}y^{13}$$

Solution Steps

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

$$3^{3}x^{3}y^{3}\times \left(4x^{3}y^{5}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{3}y^{3}\times \left(4x^{3}y^{5}\right)^{2}$$

Expand \left(4x^{3}y^{5}\right)^{2}.

$$27x^{3}y^{3}\times 4^{2}\left(x^{3}\right)^{2}\left(y^{5}\right)^{2}$$

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

$$27x^{3}y^{3}\times 4^{2}x^{6}\left(y^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$27x^{3}y^{3}\times 4^{2}x^{6}y^{10}$$

Calculate 4 to the power of 2 and get 16.

$$27x^{3}y^{3}\times 16x^{6}y^{10}$$

Multiply 27 and 16 to get 432.

$$432x^{3}y^{3}x^{6}y^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$432x^{9}y^{3}y^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$432x^{9}y^{13}$$

Expand

$$432x^{9}y^{13}$$

Solution Steps

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

$$3^{3}x^{3}y^{3}\times \left(4x^{3}y^{5}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$27x^{3}y^{3}\times \left(4x^{3}y^{5}\right)^{2}$$

Expand \left(4x^{3}y^{5}\right)^{2}.

$$27x^{3}y^{3}\times 4^{2}\left(x^{3}\right)^{2}\left(y^{5}\right)^{2}$$

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

$$27x^{3}y^{3}\times 4^{2}x^{6}\left(y^{5}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$27x^{3}y^{3}\times 4^{2}x^{6}y^{10}$$

Calculate 4 to the power of 2 and get 16.

$$27x^{3}y^{3}\times 16x^{6}y^{10}$$

Multiply 27 and 16 to get 432.

$$432x^{3}y^{3}x^{6}y^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$432x^{9}y^{3}y^{10}$$

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$432x^{9}y^{13}$$