Solve a^2/a^-4

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

Differentiate w.r.t. a

$$6a^{5}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6})$$

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}.

$$6a^{6-1}$$

Do the arithmetic.

$$6a^{5}$$

Evaluate

$$a^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from 2 to get 6.

$$a^{6}$$