Algebra Examples

$\frac{a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 1

Multiply $a$ by $a$ .

$\frac{a^{2} \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 2

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

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Step 2.1

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

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Step 2.1.1

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

$\frac{a^{2} \cdot a^{1} \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 2.1.2

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

$\frac{a^{2 + 1} \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 2.2

Add $2$ and $1$ .

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

Step 3

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

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

$\frac{a^{3 + 1} \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 3.2

Add $3$ and $1$ .

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

Step 4

Multiply $a^{4}$ by $a$ by adding the exponents.

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Step 4.1

Multiply $a^{4}$ by $a$ .

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Step 4.1.1

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

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

Step 4.1.2

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

$\frac{a^{4 + 1} \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 4.2

Add $4$ and $1$ .

$\frac{a^{5} \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 5

Multiply $a^{5}$ by $a$ by adding the exponents.

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Step 5.1

Multiply $a^{5}$ by $a$ .

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Step 5.1.1

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

$\frac{a^{5} \cdot a^{1} \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 5.1.2

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

$\frac{a^{5 + 1} \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 5.2

Add $5$ and $1$ .

$\frac{a^{6} \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 6

Multiply $a^{6}$ by $a$ by adding the exponents.

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Step 6.1

Multiply $a^{6}$ by $a$ .

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Step 6.1.1

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

$\frac{a^{6} \cdot a^{1}}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 6.1.2

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

$\frac{a^{6 + 1}}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 6.2

Add $6$ and $1$ .

$\frac{a^{7}}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$

Step 7

Multiply $a$ by $a$ .

$\frac{a^{7}}{a^{2} \cdot a \cdot a \cdot a \cdot a}$

Step 8

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

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Step 8.1

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

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Step 8.1.1

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

$\frac{a^{7}}{a^{2} \cdot a^{1} \cdot a \cdot a \cdot a}$

Step 8.1.2

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

$\frac{a^{7}}{a^{2 + 1} \cdot a \cdot a \cdot a}$

Step 8.2

Add $2$ and $1$ .

$\frac{a^{7}}{a^{3} \cdot a \cdot a \cdot a}$

Step 9

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

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Step 9.1

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

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Step 9.1.1

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

$\frac{a^{7}}{a^{3} \cdot a^{1} \cdot a \cdot a}$

Step 9.1.2

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

$\frac{a^{7}}{a^{3 + 1} \cdot a \cdot a}$

Step 9.2

Add $3$ and $1$ .

$\frac{a^{7}}{a^{4} \cdot a \cdot a}$

Step 10

Multiply $a^{4}$ by $a$ by adding the exponents.

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Step 10.1

Multiply $a^{4}$ by $a$ .

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Step 10.1.1

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

$\frac{a^{7}}{a^{4} \cdot a^{1} \cdot a}$

Step 10.1.2

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

$\frac{a^{7}}{a^{4 + 1} \cdot a}$

Step 10.2

Add $4$ and $1$ .

$\frac{a^{7}}{a^{5} \cdot a}$

Step 11

Multiply $a^{5}$ by $a$ by adding the exponents.

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Step 11.1

Multiply $a^{5}$ by $a$ .

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Step 11.1.1

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

$\frac{a^{7}}{a^{5} \cdot a^{1}}$

Step 11.1.2

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

$\frac{a^{7}}{a^{5 + 1}}$

Step 11.2

Add $5$ and $1$ .

$\frac{a^{7}}{a^{6}}$

Step 12

Cancel the common factor of $a^{7}$ and $a^{6}$ .

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Step 12.1

Factor $a^{6}$ out of $a^{7}$ .

$\frac{a^{6} a}{a^{6}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Multiply by $1$ .

$\frac{a^{6} a}{a^{6} \cdot 1}$

Step 12.2.2

Cancel the common factor.

$\frac{a^{6} a}{a^{6} \cdot 1}$

Step 12.2.3

Rewrite the expression.

$\frac{a}{1}$

Step 12.2.4

Divide $a$ by $1$ .

$a$