Solve (a^5)^2*adiva^-6

$$( a ^ { 5 } ) ^ { 2 } \cdot a \div a ^ { - 6 }$$

Evaluate

$$a^{17}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{a^{11}}{a^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from 11 to get 17.

$$a^{17}$$

Differentiate w.r.t. a

$$17a^{16}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

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

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{11}}{a^{-6}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from 11 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{17})$$

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

$$17a^{17-1}$$

Subtract 1 from 17.

$$17a^{16}$$