Find the Exact Value (27 1/3)^3

${(27 \frac{1}{3})}^{3}$

Convert $27 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

${(27 + \frac{1}{3})}^{3}$

Add $27$ and $\frac{1}{3}$ .

To write $27$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(27 \cdot \frac{3}{3} + \frac{1}{3})}^{3}$

Combine $27$ and $\frac{3}{3}$ .

${(\frac{27 \cdot 3}{3} + \frac{1}{3})}^{3}$

Combine the numerators over the common denominator.

${(\frac{27 \cdot 3 + 1}{3})}^{3}$

Simplify the numerator.

Multiply $27$ by $3$ .

${(\frac{81 + 1}{3})}^{3}$

Add $81$ and $1$ .

${(\frac{82}{3})}^{3}$

Apply the product rule to $\frac{82}{3}$ .

$\frac{82^{3}}{3^{3}}$

Raise $82$ to the power of $3$ .

$\frac{551368}{3^{3}}$

Raise $3$ to the power of $3$ .

$\frac{551368}{27}$

The result can be shown in multiple forms.

Exact Form:

$\frac{551368}{27}$

Decimal Form:

$20421.\overline{037}$

Mixed Number Form:

$20421 \frac{1}{27}$