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

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

Evaluate

$$-24z^{5}y^{10}x^{15}$$

Solution Steps

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

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

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

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

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

$$-3x^{3}yz^{2}\times 2^{3}x^{12}y^{9}z^{3}$$

Calculate 2 to the power of 3 and get 8.

$$-3x^{3}yz^{2}\times 8x^{12}y^{9}z^{3}$$

Multiply -3 and 8 to get -24.

$$-24x^{3}yz^{2}x^{12}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-24x^{15}yz^{2}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$-24x^{15}y^{10}z^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-24x^{15}y^{10}z^{5}$$

Expand

$$-24z^{5}y^{10}x^{15}$$

Solution Steps

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

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

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

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

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

$$-3x^{3}yz^{2}\times 2^{3}x^{12}y^{9}z^{3}$$

Calculate 2 to the power of 3 and get 8.

$$-3x^{3}yz^{2}\times 8x^{12}y^{9}z^{3}$$

Multiply -3 and 8 to get -24.

$$-24x^{3}yz^{2}x^{12}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-24x^{15}yz^{2}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$-24x^{15}y^{10}z^{2}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-24x^{15}y^{10}z^{5}$$