Solve 10/21x^8yz^2*14/5ax*(9/18axy)

$$\frac{ 10 }{ 21 } { x }^{ 8 } y { z }^{ 2 } \times \frac{ 14 }{ 5 } ax \times ( \frac{ 9 }{ 18 } axy)$$

Evaluate

$$\frac{2\left(ayz\right)^{2}x^{10}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{10}{21}x^{9}yz^{2}\times \frac{14}{5}a\times \frac{9}{18}axy$$

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

$$\frac{10}{21}x^{10}yz^{2}\times \frac{14}{5}a\times \frac{9}{18}ay$$

Multiply y and y to get y^{2}.

$$\frac{10}{21}x^{10}y^{2}z^{2}\times \frac{14}{5}a\times \frac{9}{18}a$$

Multiply a and a to get a^{2}.

$$\frac{10}{21}x^{10}y^{2}z^{2}\times \frac{14}{5}a^{2}\times \frac{9}{18}$$

Multiply \frac{10}{21} and \frac{14}{5} to get \frac{4}{3}.

$$\frac{4}{3}x^{10}y^{2}z^{2}a^{2}\times \frac{9}{18}$$

Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.

$$\frac{4}{3}x^{10}y^{2}z^{2}a^{2}\times \frac{1}{2}$$

Multiply \frac{4}{3} and \frac{1}{2} to get \frac{2}{3}.

$$\frac{2}{3}x^{10}y^{2}z^{2}a^{2}$$

Differentiate w.r.t. x

$$\frac{20\left(ayz\right)^{2}x^{9}}{3}$$