Solve 3a^8div1/3a^4

$$3 a ^ { 8 } \div \frac { 1 } { 3 } a ^ { 4 }$$

Evaluate

$$9a^{12}$$

Solution Steps

Divide 3a^{8} by \frac{1}{3} by multiplying 3a^{8} by the reciprocal of \frac{1}{3}.

$$3a^{8}\times 3a^{4}$$

Multiply 3 and 3 to get 9.

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

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

$$9a^{12}$$

Differentiate w.r.t. a

$$108a^{11}$$

Steps Using Definition of a Derivative

Divide 3a^{8} by \frac{1}{3} by multiplying 3a^{8} by the reciprocal of \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{8}\times 3a^{4})$$

Multiply 3 and 3 to get 9.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{12})$$

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

$$12\times 9a^{12-1}$$

Multiply 12 times 9.

$$108a^{12-1}$$

Subtract 1 from 12.

$$108a^{11}$$