Solve a^{2}a^4-a^8diva^2+a^6

$$a ^ { 2 } a ^ { 4 } - a ^ { 8 } \div a ^ { 2 } + a ^ { 6 }$$

Evaluate

$$a^{6}$$

Solution Steps

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

$$a^{6}-\frac{a^{8}}{a^{2}}+a^{6}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 8 to get 6.

$$a^{6}-a^{6}+a^{6}$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$2a^{6}-a^{6}$$

Combine 2a^{6} and -a^{6} to get a^{6}.

$$a^{6}$$

Differentiate w.r.t. a

$$6a^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}-\frac{a^{8}}{a^{2}}+a^{6})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 8 to get 6.

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

Combine a^{6} and a^{6} to get 2a^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{6}-a^{6})$$

Combine 2a^{6} and -a^{6} to get a^{6}.

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

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

$$6a^{6-1}$$

Subtract 1 from 6.

$$6a^{5}$$