Solve (4/108)^frac{2{2}}a

$$( \frac { 4 } { 108 } ) ^ { \frac { 2 } { 2 } } a$$

Evaluate

$$\frac{a}{27}$$

Solution Steps

Divide 2 by 2 to get 1.

$$\left(\frac{4}{108}\right)^{1}a$$

Reduce the fraction \frac{4}{108} to lowest terms by extracting and canceling out 4.

$$\left(\frac{1}{27}\right)^{1}a$$

Calculate \frac{1}{27} to the power of 1 and get \frac{1}{27}.

$$\frac{1}{27}a$$

Differentiate w.r.t. a

$$\frac{1}{27} = 0.037037037037037035$$

Steps Using Definition of a Derivative

Divide 2 by 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{4}{108}\right)^{1}a)$$

Reduce the fraction \frac{4}{108} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(\frac{1}{27}\right)^{1}a)$$

Calculate \frac{1}{27} to the power of 1 and get \frac{1}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{27}a)$$

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

$$\frac{1}{27}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{27}a^{0}$$

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

$$\frac{1}{27}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{27}$$