Solve 4cm2cm4cmtext{(e)}2cm3cm4cm

$$4 cm 2 cm 4 cm \text { (e) } 2 cm 3 cm 4 cm$$

Evaluate

$$8em_{2}m_{3}c^{6}\left(mm_{4}\right)^{2}$$

Solution Steps

Multiply c and c to get c^{2}.

$$4c^{2}m_{2}m_{4}cme\times 2cm_{3}cm_{4}cm$$

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

$$4c^{3}m_{2}m_{4}me\times 2cm_{3}cm_{4}cm$$

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

$$4c^{4}m_{2}m_{4}me\times 2m_{3}cm_{4}cm$$

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

$$4c^{5}m_{2}m_{4}me\times 2m_{3}m_{4}cm$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$4c^{6}m_{2}m_{4}me\times 2m_{3}m_{4}m$$

Multiply m_{4} and m_{4} to get m_{4}^{2}.

$$4c^{6}m_{2}m_{4}^{2}me\times 2m_{3}m$$

Multiply m and m to get m^{2}.

$$4c^{6}m_{2}m_{4}^{2}m^{2}e\times 2m_{3}$$

Multiply 4 and 2 to get 8.

$$8c^{6}m_{2}m_{4}^{2}m^{2}em_{3}$$

Differentiate w.r.t. m_2

$$8em_{3}c^{6}\left(mm_{4}\right)^{2}$$