Solve -5/9a^{3}xy*6/7ax^3y^2*4/5a^2xy^3=

$$- \frac { 5 } { 9 } a ^ { 3 } x y \times \frac { 6 } { 7 } a x ^ { 3 } y ^ { 2 } \times \frac { 4 } { 5 } a ^ { 2 } x y ^ { 3 } =$$

Evaluate

$$-\frac{8x^{5}\left(ay\right)^{6}}{21}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$-\frac{5}{9}a^{4}xy\times \frac{6}{7}x^{3}y^{2}\times \frac{4}{5}a^{2}xy^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-\frac{5}{9}a^{6}xy\times \frac{6}{7}x^{3}y^{2}\times \frac{4}{5}xy^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-\frac{5}{9}a^{6}x^{4}y\times \frac{6}{7}y^{2}\times \frac{4}{5}xy^{3}$$

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

$$-\frac{5}{9}a^{6}x^{5}y\times \frac{6}{7}y^{2}\times \frac{4}{5}y^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-\frac{5}{9}a^{6}x^{5}y^{3}\times \frac{6}{7}\times \frac{4}{5}y^{3}$$

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

$$-\frac{5}{9}a^{6}x^{5}y^{6}\times \frac{6}{7}\times \frac{4}{5}$$

Multiply -\frac{5}{9} and \frac{6}{7} to get -\frac{10}{21}.

$$-\frac{10}{21}a^{6}x^{5}y^{6}\times \frac{4}{5}$$

Multiply -\frac{10}{21} and \frac{4}{5} to get -\frac{8}{21}.

$$-\frac{8}{21}a^{6}x^{5}y^{6}$$

Differentiate w.r.t. x

$$-\frac{40x^{4}\left(ay\right)^{6}}{21}$$