Solve a^10/(a^2*a^4)

$$a ^ { 10 } / ( a ^ { 2 } \cdot a ^ { 4 } )$$

Evaluate

$$a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{a^{10}}{a^{6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 10 to get 4.

$$a^{4}$$

Differentiate w.r.t. a

$$4a^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{a^{6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 10 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.

$$4a^{3}$$