Solve 7x^8z^6/12x^4*7z^3/8{x^3{z}^7}

$$\frac{ 7 { x }^{ 8 } { z }^{ 6 } }{ 12 { x }^{ 4 } } \times \frac{ 7 { z }^{ 3 } }{ 8 { x }^{ 3 } { z }^{ 7 } }$$

Evaluate

$$\frac{49xz^{2}}{96}$$

Solution Steps

Cancel out x^{4} in both numerator and denominator.

$$\frac{7x^{4}z^{6}}{12}\times \frac{7z^{3}}{8x^{3}z^{7}}$$

Cancel out z^{3} in both numerator and denominator.

$$\frac{7x^{4}z^{6}}{12}\times \frac{7}{8x^{3}z^{4}}$$

Multiply \frac{7x^{4}z^{6}}{12} times \frac{7}{8x^{3}z^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7x^{4}z^{6}\times 7}{12\times 8x^{3}z^{4}}$$

Cancel out x^{3}z^{4} in both numerator and denominator.

$$\frac{7\times 7xz^{2}}{8\times 12}$$

Multiply 7 and 7 to get 49.

$$\frac{49xz^{2}}{8\times 12}$$

Multiply 8 and 12 to get 96.

$$\frac{49xz^{2}}{96}$$

Differentiate w.r.t. x

$$\frac{49z^{2}}{96}$$