Solve a^9a^3/a^6

$$\frac{ { a }^{ 9 } { a }^{ 3 } }{ { a }^{ 6 } }$$

Evaluate

$$a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{a^{12}}{a^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 12 to get 6.

$$a^{6}$$

Differentiate w.r.t. a

$$6a^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{12}}{a^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 12 to get 6.

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

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

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

Subtract 1 from 6.

$$6a^{5}$$