Solve (a^4)*(a^3)/a^4

$$\frac { ( a ^ { 4 } ) \cdot ( a ^ { 3 } ) } { a ^ { 4 } }$$

Evaluate

$$a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{a^{7}}{a^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$a^{3}$$

Differentiate w.r.t. a

$$3a^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

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

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

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

Subtract 1 from 3.

$$3a^{2}$$