Solve 9a^7*3a^3

$$9 a ^ { 7 } \times 3 a ^ { 3 }$$

Evaluate

$$27a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$9a^{10}\times 3$$

Multiply 9 and 3 to get 27.

$$27a^{10}$$

Differentiate w.r.t. a

$$270a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{10}\times 3)$$

Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(27a^{10})$$

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

$$10\times 27a^{10-1}$$

Multiply 10 times 27.

$$270a^{10-1}$$

Subtract 1 from 10.

$$270a^{9}$$