Solve frac{m^{8}*m^-2*m^4}{m^2*m^5}=

$$\frac { m ^ { 8 } \cdot m ^ { - 2 } \cdot m ^ { 4 } } { m ^ { 2 } \cdot m ^ { 5 } } =$$

Evaluate

$$m^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$\frac{m^{6}m^{4}}{m^{2}m^{5}}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{m^{10}}{m^{2}m^{5}}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{m^{10}}{m^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 10 to get 3.

$$m^{3}$$

Differentiate w.r.t. m

$$3m^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and -2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{6}m^{4}}{m^{2}m^{5}})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{10}}{m^{2}m^{5}})$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{10}}{m^{7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 10 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{3})$$

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

$$3m^{3-1}$$

Subtract 1 from 3.

$$3m^{2}$$