Basic Math Examples

$\frac{3^{3} \cdot 3^{- 4} \cdot 3^{6}}{3^{8} \cdot 3^{- 2} \cdot 3^{- 5}}$

Step 1

Multiply $3^{3}$ by $3^{- 4}$ by adding the exponents.

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Step 1.1

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

$\frac{3^{3 - 4} \cdot 3^{6}}{3^{8} \cdot 3^{- 2} \cdot 3^{- 5}}$

Step 1.2

Subtract $4$ from $3$ .

$\frac{3^{- 1} \cdot 3^{6}}{3^{8} \cdot 3^{- 2} \cdot 3^{- 5}}$

Step 2

Multiply $3^{- 1}$ by $3^{6}$ by adding the exponents.

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Step 2.1

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

$\frac{3^{- 1 + 6}}{3^{8} \cdot 3^{- 2} \cdot 3^{- 5}}$

Step 2.2

Add $- 1$ and $6$ .

$\frac{3^{5}}{3^{8} \cdot 3^{- 2} \cdot 3^{- 5}}$

Step 3

Multiply $3^{8}$ by $3^{- 2}$ by adding the exponents.

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Step 3.1

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

$\frac{3^{5}}{3^{8 - 2} \cdot 3^{- 5}}$

Step 3.2

Subtract $2$ from $8$ .

$\frac{3^{5}}{3^{6} \cdot 3^{- 5}}$

Step 4

Multiply $3^{6}$ by $3^{- 5}$ by adding the exponents.

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Step 4.1

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

$\frac{3^{5}}{3^{6 - 5}}$

Step 4.2

Subtract $5$ from $6$ .

$\frac{3^{5}}{3^{1}}$

Step 5

Simplify $3^{1}$ .

$\frac{3^{5}}{3}$

Step 6

Cancel the common factor of $3^{5}$ and $3$ .

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Step 6.1

Factor $3$ out of $3^{5}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 3^{4}}{3 (1)}$

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 6.2.4

Divide $3^{4}$ by $1$ .

$3^{4}$

Step 7

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

$81$