Solve x^{3}y^{4}z^{4}x^{2}yz^3x^2y^2z^2

$$x ^ { 3 } y ^ { 4 } z ^ { 4 } x ^ { 2 } y z ^ { 3 } x ^ { 2 } y ^ { 2 } z ^ { 2 }$$

Evaluate

$$z^{9}\left(xy\right)^{7}$$

Solution Steps

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

$$x^{5}y^{4}z^{4}yz^{3}x^{2}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{7}y^{4}z^{4}yz^{3}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{7}y^{5}z^{4}z^{3}y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$x^{7}y^{7}z^{4}z^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$x^{7}y^{7}z^{7}z^{2}$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$x^{7}y^{7}z^{9}$$

Differentiate w.r.t. x

$$7x^{6}y^{7}z^{9}$$