Solve 16m^8/4m^6*2m=

$$\frac { 16 m ^ { 8 } } { 4 m ^ { 6 } \times 2 m } =$$

Evaluate

$$2m$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{16m^{8}}{4m^{7}\times 2}$$

Cancel out 2\times 4m^{7} in both numerator and denominator.

$$2m$$

Differentiate w.r.t. m

$$2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{16}{8m}m^{8-6})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{2}{m}m^{2-1}$$

Do the arithmetic.

$$\frac{4}{m}m^{1}$$

For any term t, t^{1}=t.

$$\frac{4}{m}m$$