Pre-Algebra Examples

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

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

Step 1

Multiply

m

$m$ by

m^{3}

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

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Step 1.1

Move

m^{3}

$m^{3}$ .

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

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

Step 1.2

Multiply

m^{3}

$m^{3}$ by

m

$m$ .

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Step 1.2.1

Raise

m

$m$ to the power of

1

$1$ .

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

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

Step 1.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

\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

$3$ and

1

$1$ .

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

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

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

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

Step 2

Multiply

2

$2$ by

4

$4$ .

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

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to

2 m

$2 m$ .

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

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

Step 3.2

Raise

2

$2$ to the power of

2

$2$ .

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

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

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

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

Step 4

Cancel the common factor of

8

$8$ and

4

$4$ .

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Step 4.1

Factor

4

$4$ out of

8 m^{4}

$8 m^{4}$ .

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

4

$4$ out of

4 m^{2}

$4 m^{2}$ .

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

$1$ .

$2 m^{2}$

$2 m^{2}$

$2 m^{2}$

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