Algebra Examples

$\frac{2^{2} \cdot 3^{- 3}}{2^{- 1} \cdot 3}$

Step 1

Move $3^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2^{2}}{2^{- 1} \cdot 3 \cdot 3^{3}}$

Step 2

Multiply $3$ by $3^{3}$ by adding the exponents.

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Step 2.1

Move $3^{3}$ .

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

Step 2.2

Multiply $3^{3}$ by $3$ .

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Step 2.2.1

Raise $3$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Add $3$ and $1$ .

$\frac{2^{2}}{2^{- 1} \cdot 3^{4}}$

Step 3

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

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

Step 4

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

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Step 4.1

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

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Step 4.1.1

Raise $2$ to the power of $1$ .

$\frac{2^{2} \cdot 2^{1}}{3^{4}}$

Step 4.1.2

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

$\frac{2^{2 + 1}}{3^{4}}$

Step 4.2

Add $2$ and $1$ .

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

Step 5

Raise $2$ to the power of $3$ .

$\frac{8}{3^{4}}$

Step 6

Raise $3$ to the power of $4$ .

$\frac{8}{81}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{81}$

Decimal Form:

$0.09876543 \dots$