Evaluate (729^2+21879^227)/(39^327^2+16236243*12)

$\frac{729^{2} + 2187 \cdot 9^{2} \cdot 27}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Simplify the numerator.

Raise $729$ to the power of $2$ .

$\frac{531441 + 2187 \cdot 9^{2} \cdot 27}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Raise $9$ to the power of $2$ .

$\frac{531441 + 2187 \cdot 81 \cdot 27}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Multiply $2187$ by $81$ .

$\frac{531441 + 177147 \cdot 27}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Multiply $177147$ by $27$ .

$\frac{531441 + 4782969}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Add $531441$ and $4782969$ .

$\frac{5314410}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Simplify the denominator.

Raise $9$ to the power of $3$ .

$\frac{5314410}{3 \cdot 729 \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

Multiply $3$ by $729$ .

$\frac{5314410}{2187 \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$

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

$\frac{5314410}{2187 \cdot 729 + 162 \cdot 36 \cdot 243 \cdot 12}$

Multiply $2187$ by $729$ .

$\frac{5314410}{1594323 + 162 \cdot 36 \cdot 243 \cdot 12}$

Multiply $162$ by $36$ .

$\frac{5314410}{1594323 + 5832 \cdot 243 \cdot 12}$

Multiply $5832$ by $243$ .

$\frac{5314410}{1594323 + 1417176 \cdot 12}$

Multiply $1417176$ by $12$ .

$\frac{5314410}{1594323 + 17006112}$

Add $1594323$ and $17006112$ .

$\frac{5314410}{18600435}$

Cancel the common factor of $5314410$ and $18600435$ .

Factor $2657205$ out of $5314410$ .

$\frac{2657205 (2)}{18600435}$

Cancel the common factors.

Factor $2657205$ out of $18600435$ .

$\frac{2657205 \cdot 2}{2657205 \cdot 7}$

Cancel the common factor.

$\frac{2657205 \cdot 2}{2657205 \cdot 7}$

Rewrite the expression.

$\frac{2}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{7}$

Decimal Form:

$0.\overline{285714}$

Evaluate (729^2+2187*9^2*27)/(3*9^3*27^2+162*36*243*12)