Solve (m^4)^6m/m^12

$$\frac { ( m ^ { 4 } ) ^ { 6 } m } { m ^ { 12 } }$$

Evaluate

$$m^{13}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{m^{24}m}{m^{12}}$$

To multiply powers of the same base, add their exponents. Add 24 and 1 to get 25.

$$\frac{m^{25}}{m^{12}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 25 to get 13.

$$m^{13}$$

Differentiate w.r.t. m

$$13m^{12}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{24}m}{m^{12}})$$

To multiply powers of the same base, add their exponents. Add 24 and 1 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{25}}{m^{12}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 12 from 25 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{13})$$

The derivative of ax^{n} is nax^{n-1}.

$$13m^{13-1}$$

Subtract 1 from 13.

$$13m^{12}$$