Solve a^-4/{a^frac{2{3}}}

$$\frac{ { a }^{ -4 } }{ { a }^{ \frac{ 2 }{ 3 } } }$$

Differentiate w.r.t. a

$$-\frac{14}{3a^{\frac{17}{3}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{-4-\frac{2}{3}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{-\frac{14}{3}})$$

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}.

$$-\frac{14}{3}a^{-\frac{14}{3}-1}$$

Do the arithmetic.

$$-\frac{14}{3}a^{-\frac{17}{3}}$$

Evaluate

$$\frac{1}{a^{\frac{14}{3}}}$$