Basic Math Examples

$\frac{81^{2} \cdot 27^{3} \cdot 9^{4}}{243^{6}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\frac{{(3^{4})}^{2} \cdot 27^{3} \cdot 9^{4}}{243^{6}}$

Step 1.2

Multiply the exponents in ${(3^{4})}^{2}$ .

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Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{4 \cdot 2} \cdot 27^{3} \cdot 9^{4}}{243^{6}}$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{3^{8} \cdot 27^{3} \cdot 9^{4}}{243^{6}}$

Step 1.3

Rewrite $27$ as $3^{3}$ .

$\frac{3^{8} \cdot {(3^{3})}^{3} \cdot 9^{4}}{243^{6}}$

Step 1.4

Multiply the exponents in ${(3^{3})}^{3}$ .

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Step 1.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{8} \cdot 3^{3 \cdot 3} \cdot 9^{4}}{243^{6}}$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{3^{8} \cdot 3^{9} \cdot 9^{4}}{243^{6}}$

Step 1.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3^{8 + 9} \cdot 9^{4}}{243^{6}}$

Step 1.6

Add $8$ and $9$ .

$\frac{3^{17} \cdot 9^{4}}{243^{6}}$

Step 1.7

Rewrite $9$ as $3^{2}$ .

$\frac{3^{17} \cdot {(3^{2})}^{4}}{243^{6}}$

Step 1.8

Multiply the exponents in ${(3^{2})}^{4}$ .

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Step 1.8.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{17} \cdot 3^{2 \cdot 4}}{243^{6}}$

Step 1.8.2

Multiply $2$ by $4$ .

$\frac{3^{17} \cdot 3^{8}}{243^{6}}$

Step 1.9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3^{17 + 8}}{243^{6}}$

Step 1.10

Add $17$ and $8$ .

$\frac{3^{25}}{243^{6}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Raise $243$ to the power of $6$ .

$\frac{3^{25}}{205891132094649}$

Step 2.2

Raise $3$ to the power of $25$ .

$\frac{847288609443}{205891132094649}$

Step 2.3

Cancel the common factor of $847288609443$ and $205891132094649$ .

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Step 2.3.1

Factor $847288609443$ out of $847288609443$ .

$\frac{847288609443 (1)}{205891132094649}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $847288609443$ out of $205891132094649$ .

$\frac{847288609443 \cdot 1}{847288609443 \cdot 243}$

Step 2.3.2.2

Cancel the common factor.

$\frac{847288609443 \cdot 1}{847288609443 \cdot 243}$

Step 2.3.2.3

Rewrite the expression.

$\frac{1}{243}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{243}$

Decimal Form:

$0.00411522 \dots$