Solve (a^{3})^{2}+a^3*a^2-a^3diva^-2

$$( a ^ { 3 } ) ^ { 2 } + a ^ { 3 } \cdot a ^ { 2 } - a ^ { 3 } \div a ^ { - 2 }$$

Evaluate

$$a^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}+a^{3}a^{2}-\frac{a^{3}}{a^{-2}}$$

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

$$a^{6}+a^{5}-\frac{a^{3}}{a^{-2}}$$

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

$$a^{6}+a^{5}-a^{5}$$

Subtract a^{5} from a^{5} to get 0.

$$a^{6}$$

Differentiate w.r.t. a

$$6a^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{3}a^{2}-\frac{a^{3}}{a^{-2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{5}-\frac{a^{3}}{a^{-2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{5}-a^{5})$$

Subtract a^{5} from a^{5} to get 0.

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

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

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

Subtract 1 from 6.

$$6a^{5}$$