Solve a^3*a^10/a^-2

$$\frac { a ^ { 3 } \times a ^ { 10 } } { a ^ { - 2 } }$$

Evaluate

$$a^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$\frac{a^{13}}{a^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 13 to get 15.

$$a^{15}$$

Differentiate w.r.t. a

$$15a^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{13}}{a^{-2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 13 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{15})$$

The derivative of ax^{n} is nax^{n-1}.

$$15a^{15-1}$$

Subtract 1 from 15.

$$15a^{14}$$