Solve d^-12/d^-4?

$$\frac { d ^ { - 12 } } { d ^ { - 4 } } ?$$

Differentiate w.r.t. d

$$-\frac{8}{d^{9}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{1}d^{-12-\left(-4\right)})$$

Do the arithmetic.

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

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}.

$$-8d^{-8-1}$$

Do the arithmetic.

$$-8d^{-9}$$

Evaluate

$$\frac{1}{d^{8}}$$

Solution Steps

Rewrite d^{-4} as d^{-12}d^{8}. Cancel out d^{-12} in both numerator and denominator.

$$\frac{1}{d^{8}}$$