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

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

Evaluate

$$\frac{mx^{4}a^{6}}{5}$$

Solution Steps

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

$$\frac{1}{2}x^{4}\times \frac{-2}{3}a^{2}\times \frac{-3}{5}a^{4}m$$

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

$$\frac{1}{2}x^{4}\times \frac{-2}{3}a^{6}\times \frac{-3}{5}m$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

$$-\frac{1}{3}x^{4}a^{6}\times \frac{-3}{5}m$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

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

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

$$\frac{1}{5}x^{4}a^{6}m$$

Differentiate w.r.t. x

$$\frac{4mx^{3}a^{6}}{5}$$