Evaluate (27^2)/27 4/3

$\frac{27^{2}}{27 \frac{4}{3}}$

Step 1

Convert $27 \frac{4}{3}$ to an improper fraction.

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

$\frac{27^{2}}{27 + \frac{4}{3}}$

Add $27$ and $\frac{4}{3}$ .

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

$\frac{27^{2}}{27 \cdot \frac{3}{3} + \frac{4}{3}}$

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

$\frac{27^{2}}{\frac{27 \cdot 3}{3} + \frac{4}{3}}$

Combine the numerators over the common denominator.

$\frac{27^{2}}{\frac{27 \cdot 3 + 4}{3}}$

Simplify the numerator.

Multiply $27$ by $3$ .

$\frac{27^{2}}{\frac{81 + 4}{3}}$

Add $81$ and $4$ .

$\frac{27^{2}}{\frac{85}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$27^{2} \frac{3}{85}$

Step 3

Raise $27$ to the power of $2$ .

$729 (\frac{3}{85})$

Step 4

Multiply $729 (\frac{3}{85})$ .

Combine $729$ and $\frac{3}{85}$ .

$\frac{729 \cdot 3}{85}$

Multiply $729$ by $3$ .

$\frac{2187}{85}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2187}{85}$

Decimal Form:

$25.72941176 \dots$

Mixed Number Form:

$25 \frac{62}{85}$