Solve a^4*a^6/a^2=

$$\frac { a ^ { 4 } \times a ^ { 6 } } { a ^ { 2 } } =$$

Evaluate

$$a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{a^{10}}{a^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{10}}{a^{2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8})$$

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

$$8a^{8-1}$$

Subtract 1 from 8.

$$8a^{7}$$