Solve |-25/6|a^2c^2*12/3ac^2

$$| - 2 \frac { 5 } { 6 } | a ^ { 2 } c ^ { 2 } \cdot 1 \frac { 2 } { 3 } a c ^ { 2 }$$

Evaluate

$$\frac{85a^{3}c^{4}}{18}$$

Solution Steps

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

$$|-\frac{2\times 6+5}{6}|a^{3}c^{2}\times \frac{1\times 3+2}{3}c^{2}$$

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

$$|-\frac{2\times 6+5}{6}|a^{3}c^{4}\times \frac{1\times 3+2}{3}$$

Multiply 2 and 6 to get 12.

$$|-\frac{12+5}{6}|a^{3}c^{4}\times \frac{1\times 3+2}{3}$$

Add 12 and 5 to get 17.

$$|-\frac{17}{6}|a^{3}c^{4}\times \frac{1\times 3+2}{3}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{17}{6} is \frac{17}{6}.

$$\frac{17}{6}a^{3}c^{4}\times \frac{1\times 3+2}{3}$$

Multiply 1 and 3 to get 3.

$$\frac{17}{6}a^{3}c^{4}\times \frac{3+2}{3}$$

Add 3 and 2 to get 5.

$$\frac{17}{6}a^{3}c^{4}\times \frac{5}{3}$$

Multiply \frac{17}{6} and \frac{5}{3} to get \frac{85}{18}.

$$\frac{85}{18}a^{3}c^{4}$$

Differentiate w.r.t. a

$$\frac{85a^{2}c^{4}}{6}$$