Solve 3^26a^9/9^2}^9

$$\frac { 3 ^ { 26 } a ^ { 9 } } { 9 ^ { 2 } } \} ^ { 9 }$$

Evaluate

$$31381059609a^{9}$$

Solution Steps

Calculate 3 to the power of 26 and get 2541865828329.

$$\frac{2541865828329a^{9}}{9^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{2541865828329a^{9}}{81}$$

Divide 2541865828329a^{9} by 81 to get 31381059609a^{9}.

$$31381059609a^{9}$$

Differentiate w.r.t. a

$$282429536481a^{8}$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 26 and get 2541865828329.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2541865828329a^{9}}{9^{2}})$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2541865828329a^{9}}{81})$$

Divide 2541865828329a^{9} by 81 to get 31381059609a^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(31381059609a^{9})$$

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

$$9\times 31381059609a^{9-1}$$

Multiply 9 times 31381059609.

$$282429536481a^{9-1}$$

Subtract 1 from 9.

$$282429536481a^{8}$$