Solve m^-3/m^-2

$$\frac { m ^ { - 3 } } { m ^ { - 2 } }$$

Differentiate w.r.t. m

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

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{m})$$

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}.

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

Do the arithmetic.

$$-m^{-2}$$

Evaluate

$$\frac{1}{m}$$

Solution Steps

Rewrite m^{-2} as m^{-3}m. Cancel out m^{-3} in both numerator and denominator.

$$\frac{1}{m}$$