Solve a^-16diva^-6

$$a ^ { - 16 } \div a ^ { - 6 }$$

Differentiate w.r.t. a

$$-\frac{10}{a^{11}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{-16-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{-10})$$

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}.

$$-10a^{-10-1}$$

Do the arithmetic.

$$-10a^{-11}$$

Evaluate

$$\frac{1}{a^{10}}$$

Solution Steps

Rewrite a^{-6} as a^{-16}a^{10}. Cancel out a^{-16} in both numerator and denominator.

$$\frac{1}{a^{10}}$$