Solve a^5*4a^2*3a^0

$$a ^ { 5 } \cdot 4 a ^ { 2 } \cdot 3 a ^ { 0 }$$

Evaluate

$$12a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$a^{7}\times 4\times 3a^{0}$$

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$a^{7}\times 4\times 3$$

Multiply 4 and 3 to get 12.

$$a^{7}\times 12$$

Differentiate w.r.t. a

$$84a^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}\times 4\times 3a^{0})$$

To multiply powers of the same base, add their exponents. Add 7 and 0 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}\times 4\times 3)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{7}\times 12)$$

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

$$7\times 12a^{7-1}$$

Multiply 7 times 12.

$$84a^{7-1}$$

Subtract 1 from 7.

$$84a^{6}$$