Solve (1/2x^3)(-2/3a^2x)(-3/5a^4x^2)

$$( \frac { 1 } { 2 } x ^ { 3 } ) ( - \frac { 2 } { 3 } a ^ { 2 } x ) ( - \frac { 3 } { 5 } a ^ { 4 } x ^ { 2 } )$$

Evaluate

$$\frac{\left(ax\right)^{6}}{5}$$

Solution Steps

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

$$\frac{1}{2}x^{4}\left(-\frac{2}{3}\right)a^{2}\left(-\frac{3}{5}\right)a^{4}x^{2}$$

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

$$\frac{1}{2}x^{6}\left(-\frac{2}{3}\right)a^{2}\left(-\frac{3}{5}\right)a^{4}$$

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

$$\frac{1}{2}x^{6}\left(-\frac{2}{3}\right)a^{6}\left(-\frac{3}{5}\right)$$

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

$$-\frac{1}{3}x^{6}a^{6}\left(-\frac{3}{5}\right)$$

Multiply -\frac{1}{3} and -\frac{3}{5} to get \frac{1}{5}.

$$\frac{1}{5}x^{6}a^{6}$$

Differentiate w.r.t. x

$$\frac{6x^{5}a^{6}}{5}$$