Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $2187 \cdot 81 \cdot 27$ .

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Step 1.3.1

Multiply $2187$ by $81$ .

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

Step 1.3.2

Multiply $177147$ by $27$ .

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

Step 1.4

Add $531441$ and $4782969$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Multiply $3$ by $729$ .

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

Step 2.3

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

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

Step 2.4

Multiply $2187$ by $729$ .

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

Step 2.5

Multiply $162 \cdot 36 \cdot 243 \cdot 12$ .

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Step 2.5.1

Multiply $162$ by $36$ .

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

Step 2.5.2

Multiply $5832$ by $243$ .

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

Step 2.5.3

Multiply $1417176$ by $12$ .

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

Step 2.6

Add $1594323$ and $17006112$ .

$\frac{5314410}{18600435}$

Step 3

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

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Step 3.1

Factor $2657205$ out of $5314410$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2657205$ out of $18600435$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{2}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{7}$

Decimal Form:

$0.\overline{285714}$