Pre-Algebra Examples

$\frac{(4 m) (2 m^{3})}{{(2 m)}^{2}}$

Step 1

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

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Step 1.1

Move $m^{3}$ .

$\frac{4 (m^{3} m) \cdot 2}{{(2 m)}^{2}}$

Step 1.2

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

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Step 1.2.1

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

$\frac{4 (m^{3} m^{1}) \cdot 2}{{(2 m)}^{2}}$

Step 1.2.2

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

$\frac{4 m^{3 + 1} \cdot 2}{{(2 m)}^{2}}$

$\frac{4 m^{3 + 1} \cdot 2}{{(2 m)}^{2}}$

Step 1.3

Add $3$ and $1$ .

$\frac{4 m^{4} \cdot 2}{{(2 m)}^{2}}$

$\frac{4 m^{4} \cdot 2}{{(2 m)}^{2}}$

Step 2

Multiply $2$ by $4$ .

$\frac{8 m^{4}}{{(2 m)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $2 m$ .

$\frac{8 m^{4}}{2^{2} m^{2}}$

Step 3.2

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

$\frac{8 m^{4}}{4 m^{2}}$

$\frac{8 m^{4}}{4 m^{2}}$

Step 4

Cancel the common factor of $8$ and $4$ .

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Step 4.1

Factor $4$ out of $8 m^{4}$ .

$\frac{4 (2 m^{4})}{4 m^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $4 m^{2}$ .

$\frac{4 (2 m^{4})}{4 (m^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{4 (2 m^{4})}{4 m^{2}}$

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $m^{4}$ and $m^{2}$ .

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Step 5.1

Factor $m^{2}$ out of $2 m^{4}$ .

$\frac{m^{2} (2 m^{2})}{m^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{2 m^{2}}{1}$

Step 5.2.4

Divide $2 m^{2}$ by $1$ .

$2 m^{2}$

$2 m^{2}$

$2 m^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$