Solve (6x^{2}yz^{3})(2x^4y^3z^2)^4

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

Evaluate

$$96z^{11}y^{13}x^{18}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$6x^{2}yz^{3}\times 2^{4}x^{16}\left(y^{3}\right)^{4}\left(z^{2}\right)^{4}$$

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

$$6x^{2}yz^{3}\times 2^{4}x^{16}y^{12}\left(z^{2}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$6x^{2}yz^{3}\times 2^{4}x^{16}y^{12}z^{8}$$

Calculate 2 to the power of 4 and get 16.

$$6x^{2}yz^{3}\times 16x^{16}y^{12}z^{8}$$

Multiply 6 and 16 to get 96.

$$96x^{2}yz^{3}x^{16}y^{12}z^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 16 to get 18.

$$96x^{18}yz^{3}y^{12}z^{8}$$

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

$$96x^{18}y^{13}z^{3}z^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$96x^{18}y^{13}z^{11}$$

Expand

$$96z^{11}y^{13}x^{18}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$6x^{2}yz^{3}\times 2^{4}x^{16}\left(y^{3}\right)^{4}\left(z^{2}\right)^{4}$$

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

$$6x^{2}yz^{3}\times 2^{4}x^{16}y^{12}\left(z^{2}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$6x^{2}yz^{3}\times 2^{4}x^{16}y^{12}z^{8}$$

Calculate 2 to the power of 4 and get 16.

$$6x^{2}yz^{3}\times 16x^{16}y^{12}z^{8}$$

Multiply 6 and 16 to get 96.

$$96x^{2}yz^{3}x^{16}y^{12}z^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 16 to get 18.

$$96x^{18}yz^{3}y^{12}z^{8}$$

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

$$96x^{18}y^{13}z^{3}z^{8}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$96x^{18}y^{13}z^{11}$$