Basic Math Examples

$\frac{9^{2} \cdot 9 \cdot 9^{6}}{9^{5} \cdot 9^{3}}$

Step 1

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

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Step 1.1

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

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Step 1.1.1

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

$\frac{9^{2} \cdot 9^{1} \cdot 9^{6}}{9^{5} \cdot 9^{3}}$

Step 1.1.2

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

$\frac{9^{2 + 1} \cdot 9^{6}}{9^{5} \cdot 9^{3}}$

Step 1.2

Add $2$ and $1$ .

$\frac{9^{3} \cdot 9^{6}}{9^{5} \cdot 9^{3}}$

Step 2

Multiply $9^{3}$ by $9^{6}$ 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.

$\frac{9^{3 + 6}}{9^{5} \cdot 9^{3}}$

Step 2.2

Add $3$ and $6$ .

$\frac{9^{9}}{9^{5} \cdot 9^{3}}$

Step 3

Multiply $9^{5}$ by $9^{3}$ 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.

$\frac{9^{9}}{9^{5 + 3}}$

Step 3.2

Add $5$ and $3$ .

$\frac{9^{9}}{9^{8}}$

Step 4

Cancel the common factor of $9^{9}$ and $9^{8}$ .

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Step 4.1

Factor $9^{8}$ out of $9^{9}$ .

$\frac{9^{8} \cdot 9}{9^{8}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{9^{8} \cdot 9}{9^{8} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{9^{8} \cdot 9}{9^{8} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{9}{1}$

Step 4.2.4

Divide $9$ by $1$ .

$9$