Solve (m^5)^4m/m^10

$$\frac { ( m ^ { 5 } ) ^ { 4 } m } { m ^ { 10 } }$$

Evaluate

$$m^{11}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{m^{20}m}{m^{10}}$$

To multiply powers of the same base, add their exponents. Add 20 and 1 to get 21.

$$\frac{m^{21}}{m^{10}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 21 to get 11.

$$m^{11}$$

Differentiate w.r.t. m

$$11m^{10}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{20}m}{m^{10}})$$

To multiply powers of the same base, add their exponents. Add 20 and 1 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{21}}{m^{10}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 21 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{11})$$

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

$$11m^{11-1}$$

Subtract 1 from 11.

$$11m^{10}$$