Solve 9a^4*4a^4

$$9 a ^ { 4 } \times 4 a ^ { 4 }$$

Evaluate

$$36a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$9a^{8}\times 4$$

Multiply 9 and 4 to get 36.

$$36a^{8}$$

Differentiate w.r.t. a

$$288a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{8}\times 4)$$

Multiply 9 and 4 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}a}(36a^{8})$$

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

$$8\times 36a^{8-1}$$

Multiply 8 times 36.

$$288a^{8-1}$$

Subtract 1 from 8.

$$288a^{7}$$