Pre-Algebra Examples

$\frac{6 m n}{(4 m^{3} n) (20 m n)}$

Step 1

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

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Step 1.1

Move $m$ .

$\frac{6 m n}{4 (m \cdot m^{3}) n (20 n)}$

Step 1.2

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

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Step 1.2.1

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

$\frac{6 m n}{4 (m^{1} m^{3}) n (20 n)}$

Step 1.2.2

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

$\frac{6 m n}{4 m^{1 + 3} n (20 n)}$

$\frac{6 m n}{4 m^{1 + 3} n (20 n)}$

Step 1.3

Add $1$ and $3$ .

$\frac{6 m n}{4 m^{4} n (20 n)}$

$\frac{6 m n}{4 m^{4} n (20 n)}$

Step 2

Multiply $n$ by $n$ by adding the exponents.

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Step 2.1

Move $n$ .

$\frac{6 m n}{4 m^{4} (n \cdot n) \cdot 20}$

Step 2.2

Multiply $n$ by $n$ .

$\frac{6 m n}{4 m^{4} n^{2} \cdot 20}$

$\frac{6 m n}{4 m^{4} n^{2} \cdot 20}$

Step 3

Cancel the common factor of $6$ and $4$ .

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Step 3.1

Factor $2$ out of $6 m n$ .

$\frac{2 (3 m n)}{4 m^{4} n^{2} \cdot 20}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4 m^{4} n^{2} \cdot 20$ .

$\frac{2 (3 m n)}{2 (2 m^{4} n^{2} \cdot 20)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (3 m n)}{2 (2 m^{4} n^{2} \cdot 20)}$

Step 3.2.3

Rewrite the expression.

$\frac{3 m n}{2 m^{4} n^{2} \cdot 20}$

$\frac{3 m n}{2 m^{4} n^{2} \cdot 20}$

$\frac{3 m n}{2 m^{4} n^{2} \cdot 20}$

Step 4

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

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Step 4.1

Factor $m$ out of $3 m n$ .

$\frac{m (3 n)}{2 m^{4} n^{2} \cdot 20}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m$ out of $2 m^{4} n^{2} \cdot 20$ .

$\frac{m (3 n)}{m (2 m^{3} n^{2} \cdot 20)}$

Step 4.2.2

Cancel the common factor.

$\frac{m (3 n)}{m (2 m^{3} n^{2} \cdot 20)}$

Step 4.2.3

Rewrite the expression.

$\frac{3 n}{2 m^{3} n^{2} \cdot 20}$

$\frac{3 n}{2 m^{3} n^{2} \cdot 20}$

$\frac{3 n}{2 m^{3} n^{2} \cdot 20}$

Step 5

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

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Step 5.1

Factor $n$ out of $3 n$ .

$\frac{n \cdot 3}{2 m^{3} n^{2} \cdot 20}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $n$ out of $2 m^{3} n^{2} \cdot 20$ .

$\frac{n \cdot 3}{n (2 m^{3} n \cdot 20)}$

Step 5.2.2

Cancel the common factor.

$\frac{n \cdot 3}{n (2 m^{3} n \cdot 20)}$

Step 5.2.3

Rewrite the expression.

$\frac{3}{2 m^{3} n \cdot 20}$

$\frac{3}{2 m^{3} n \cdot 20}$

$\frac{3}{2 m^{3} n \cdot 20}$

Step 6

Multiply $20$ by $2$ .

$\frac{3}{40 m^{3} n}$

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