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

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

Evaluate

$$a^{6}+a^{5}-a-3$$

Solution Steps

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

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

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$a^{6}+a^{5}-a^{1}-3$$

Calculate a to the power of 1 and get a.

$$a^{6}+a^{5}-a-3$$

Differentiate w.r.t. a

$$6a^{5}+5a^{4}-1$$

Steps Using Derivative Rule for Sum

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

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

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{5}-a^{1}-3)$$

Calculate a to the power of 1 and get a.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$6a^{6-1}+5a^{5-1}-a^{1-1}$$

Subtract 1 from 6.

$$6a^{5}+5a^{5-1}-a^{1-1}$$

Subtract 1 from 5.

$$6a^{5}+5a^{4}-a^{1-1}$$

Subtract 1 from 1.

$$6a^{5}+5a^{4}-a^{0}$$

For any term t except 0, t^{0}=1.

$$6a^{5}+5a^{4}-1$$