Solve 16a^2div4a^2

$$16 a ^ { 2 } \div 4 a ^ { 2 }$$

Evaluate

$$4a^{4}$$

Solution Steps

Divide 16a^{2} by 4 to get 4a^{2}.

$$4a^{2}a^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$4a^{4}$$

Differentiate w.r.t. a

$$16a^{3}$$

Steps Using Definition of a Derivative

Divide 16a^{2} by 4 to get 4a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{2}a^{2})$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

$$4\times 4a^{4-1}$$

Multiply 4 times 4.

$$16a^{4-1}$$

Subtract 1 from 4.

$$16a^{3}$$