Solve a^2/aa^3

$$\frac { a ^ { 2 } } { a } a ^ { 3 }$$

Evaluate

$$a^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$a^{1}a^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$a^{4}$$

Differentiate w.r.t. a

$$4a^{3}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{1}a^{3})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

Subtract 1 from 4.

$$4a^{3}$$