Basic Math Examples

$\frac{{(9^{2} \cdot 81)}^{- 1} \cdot 3}{27^{- 2} \cdot 9}$

Step 1

Move ${(9^{2} \cdot 81)}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3}{27^{- 2} \cdot 9 (9^{2} \cdot 81)}$

Step 2

Multiply $9$ by $9^{2}$ by adding the exponents.

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Step 2.1

Move $9^{2}$ .

$\frac{3}{27^{- 2} \cdot (9^{2} \cdot 9) \cdot 81}$

Step 2.2

Multiply $9^{2}$ by $9$ .

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Step 2.2.1

Raise $9$ to the power of $1$ .

$\frac{3}{27^{- 2} \cdot (9^{2} \cdot 9^{1}) \cdot 81}$

Step 2.2.2

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

$\frac{3}{27^{- 2} \cdot 9^{2 + 1} \cdot 81}$

Step 2.3

Add $2$ and $1$ .

$\frac{3}{27^{- 2} \cdot 9^{3} \cdot 81}$

Step 3

Move $27^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

Cancel the common factor of $3$ and $81$ .

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Step 4.1

Factor $3$ out of $3 \cdot 27^{2}$ .

$\frac{3 (27^{2})}{9^{3} \cdot 81}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $9^{3} \cdot 81$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{27^{2}}{9^{3} \cdot 27}$

Step 5

Cancel the common factor of $27^{2}$ and $27$ .

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Step 5.1

Factor $27$ out of $27^{2}$ .

$\frac{27 \cdot 27}{9^{3} \cdot 27}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $27$ out of $9^{3} \cdot 27$ .

$\frac{27 \cdot 27}{27 \cdot 9^{3}}$

Step 5.2.2

Cancel the common factor.

$\frac{27 \cdot 27}{27 \cdot 9^{3}}$

Step 5.2.3

Rewrite the expression.

$\frac{27}{9^{3}}$

Step 6

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

$\frac{27}{729}$

Step 7

Cancel the common factor of $27$ and $729$ .

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Step 7.1

Factor $27$ out of $27$ .

$\frac{27 (1)}{729}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $27$ out of $729$ .

$\frac{27 \cdot 1}{27 \cdot 27}$

Step 7.2.2

Cancel the common factor.

$\frac{27 \cdot 1}{27 \cdot 27}$

Step 7.2.3

Rewrite the expression.

$\frac{1}{27}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{27}$

Decimal Form:

$0.\overline{037}$