Solve 6*2x^3*y^4*z^2*7/4*x^3*{y}^4*{z}^2

$$6 \times 2 { x }^{ 3 } \times { y }^{ 4 } \times { z }^{ 2 } \times \frac{ 7 }{ 4 } \times { x }^{ 3 } \times { y }^{ 4 } \times { z }^{ 2 }$$

Evaluate

$$21z^{4}x^{6}y^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$6\times 2x^{6}y^{4}z^{2}\times \frac{7}{4}y^{4}z^{2}$$

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

$$6\times 2x^{6}y^{8}z^{2}\times \frac{7}{4}z^{2}$$

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

$$6\times 2x^{6}y^{8}z^{4}\times \frac{7}{4}$$

Multiply 6 and 2 to get 12.

$$12x^{6}y^{8}z^{4}\times \frac{7}{4}$$

Multiply 12 and \frac{7}{4} to get 21.

$$21x^{6}y^{8}z^{4}$$

Differentiate w.r.t. x

$$126z^{4}x^{5}y^{8}$$