Solve (5x^{4}y^{2}z^2)(3x^4y^3z^5)

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

Evaluate

$$15y^{5}z^{7}x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$5x^{8}y^{2}z^{2}\times 3y^{3}z^{5}$$

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

$$5x^{8}y^{5}z^{2}\times 3z^{5}$$

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

$$5x^{8}y^{5}z^{7}\times 3$$

Multiply 5 and 3 to get 15.

$$15x^{8}y^{5}z^{7}$$

Differentiate w.r.t. x

$$120y^{5}\left(xz\right)^{7}$$