Solve a^13diva^7*a^3

$$a ^ { 13 } \div a ^ { 7 } \cdot a ^ { 3 }$$

Evaluate

$$a^{9}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 13 to get 6.

$$a^{6}a^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$a^{9}$$

Differentiate w.r.t. a

$$9a^{8}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 13 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}a^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9})$$

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

$$9a^{9-1}$$

Subtract 1 from 9.

$$9a^{8}$$