Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

Move $a^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $2$ and $1$ .

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

Step 4

Simplify the expression.

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Step 4.1

Simplify $a^{3} \cdot 1$ .

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

Step 4.2

Multiply $a$ by $1$ .

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

Step 4.3

Multiply $a$ by $a$ .

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

Step 5

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Step 5.1

Factor $a^{2}$ out of $a^{3}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{a}{1}$

Step 5.2.4

Divide $a$ by $1$ .

$a$