Solve d[(1/3-1/9)^2+(1/3)^3]:(1/3)

$$d [ ( \frac { 1 } { 3 } - \frac { 1 } { 9 } ) ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 3 } ] : ( \frac { 1 } { 3 } )$$

Evaluate

$$\frac{7d}{27}$$

Solution Steps

Subtract \frac{1}{9} from \frac{1}{3} to get \frac{2}{9}.

$$\frac{d\left(\left(\frac{2}{9}\right)^{2}+\left(\frac{1}{3}\right)^{3}\right)}{\frac{1}{3}}$$

Calculate \frac{2}{9} to the power of 2 and get \frac{4}{81}.

$$\frac{d\left(\frac{4}{81}+\left(\frac{1}{3}\right)^{3}\right)}{\frac{1}{3}}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{d\left(\frac{4}{81}+\frac{1}{27}\right)}{\frac{1}{3}}$$

Add \frac{4}{81} and \frac{1}{27} to get \frac{7}{81}.

$$\frac{d\times \frac{7}{81}}{\frac{1}{3}}$$

Divide d\times \frac{7}{81} by \frac{1}{3} by multiplying d\times \frac{7}{81} by the reciprocal of \frac{1}{3}.

$$d\times \frac{7}{81}\times 3$$

Multiply \frac{7}{81} and 3 to get \frac{7}{27}.

$$d\times \frac{7}{27}$$

Expand

$$\frac{7d}{27}$$

Solution Steps

Subtract \frac{1}{9} from \frac{1}{3} to get \frac{2}{9}.

$$\frac{d\left(\left(\frac{2}{9}\right)^{2}+\left(\frac{1}{3}\right)^{3}\right)}{\frac{1}{3}}$$

Calculate \frac{2}{9} to the power of 2 and get \frac{4}{81}.

$$\frac{d\left(\frac{4}{81}+\left(\frac{1}{3}\right)^{3}\right)}{\frac{1}{3}}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{d\left(\frac{4}{81}+\frac{1}{27}\right)}{\frac{1}{3}}$$

Add \frac{4}{81} and \frac{1}{27} to get \frac{7}{81}.

$$\frac{d\times \frac{7}{81}}{\frac{1}{3}}$$

Divide d\times \frac{7}{81} by \frac{1}{3} by multiplying d\times \frac{7}{81} by the reciprocal of \frac{1}{3}.

$$d\times \frac{7}{81}\times 3$$

Multiply \frac{7}{81} and 3 to get \frac{7}{27}.

$$d\times \frac{7}{27}$$