Solve a^5diva^3*a^2=

$$a ^ { 5 } \div a ^ { 3 } \cdot a ^ { 2 } =$$

Evaluate

$$a^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 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 3 from 5 to get 2.

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

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

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

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

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

Subtract 1 from 4.

$$4a^{3}$$