Solve -1/2abc*2/3a^2b^2*(-3/5)bc^2

$$- \frac { 1 } { 2 } a b c \cdot \frac { 2 } { 3 } a ^ { 2 } b ^ { 2 } \cdot ( - \frac { 3 } { 5 } ) b c ^ { 2 }$$

Evaluate

$$\frac{b^{4}\left(ac\right)^{3}}{5}$$

Solution Steps

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

$$-\frac{1}{2}a^{3}bc\times \frac{2}{3}b^{2}\left(-\frac{3}{5}\right)bc^{2}$$

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

$$-\frac{1}{2}a^{3}b^{3}c\times \frac{2}{3}\left(-\frac{3}{5}\right)bc^{2}$$

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

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

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

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

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

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

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

$$\frac{1}{5}a^{3}b^{4}c^{3}$$

Differentiate w.r.t. a

$$\frac{3a^{2}c^{3}b^{4}}{5}$$