Solve m^4*m^-3*m/(m^-2)^3=

$$\frac { m ^ { 4 } \cdot m ^ { - 3 } \cdot m } { ( m ^ { - 2 } ) ^ { 3 } } =$$

Evaluate

$$m^{8}$$

Solution Steps

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

$$\frac{m^{1}m}{\left(m^{-2}\right)^{3}}$$

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

$$\frac{m^{2}}{\left(m^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{m^{2}}{m^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from 2 to get 8.

$$m^{8}$$

Differentiate w.r.t. m

$$8m^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{1}m}{\left(m^{-2}\right)^{3}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{2}}{\left(m^{-2}\right)^{3}})$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from 2 to get 8.

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

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

$$8m^{8-1}$$

Subtract 1 from 8.

$$8m^{7}$$