Solve a^5/a^-3

$$\frac { a ^ { 5 } } { a ^ { - 3 } }$$

Differentiate w.r.t. a

$$8a^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{5-\left(-3\right)})$$

Do the arithmetic.

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

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}.

$$8a^{8-1}$$

Do the arithmetic.

$$8a^{7}$$

Evaluate

$$a^{8}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 5 to get 8.

$$a^{8}$$