Solve (4a^8)*(5a^4)

$$( 4 a ^ { 8 } ) \cdot ( 5 a ^ { 4 } )$$

Evaluate

$$20a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

$$4a^{12}\times 5$$

Multiply 4 and 5 to get 20.

$$20a^{12}$$

Differentiate w.r.t. a

$$240a^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{12}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20a^{12})$$

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

$$12\times 20a^{12-1}$$

Multiply 12 times 20.

$$240a^{12-1}$$

Subtract 1 from 12.

$$240a^{11}$$