Solve (2x^2y)(6xy^3)^4

$$( 2 x ^ { 2 } y ) ( 6 x y ^ { 3 } ) ^ { 4 }$$

Evaluate

$$2592x^{6}y^{13}$$

Solution Steps

Expand \left(6xy^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$2x^{2}y\times 6^{4}x^{4}y^{12}$$

Calculate 6 to the power of 4 and get 1296.

$$2x^{2}y\times 1296x^{4}y^{12}$$

Multiply 2 and 1296 to get 2592.

$$2592x^{2}yx^{4}y^{12}$$

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

$$2592x^{6}yy^{12}$$

To multiply powers of the same base, add their exponents. Add 1 and 12 to get 13.

$$2592x^{6}y^{13}$$

Expand

$$2592x^{6}y^{13}$$

Solution Steps

Expand \left(6xy^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$2x^{2}y\times 6^{4}x^{4}y^{12}$$

Calculate 6 to the power of 4 and get 1296.

$$2x^{2}y\times 1296x^{4}y^{12}$$

Multiply 2 and 1296 to get 2592.

$$2592x^{2}yx^{4}y^{12}$$

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

$$2592x^{6}yy^{12}$$

To multiply powers of the same base, add their exponents. Add 1 and 12 to get 13.

$$2592x^{6}y^{13}$$