Basic Math Examples

$\frac{3 z^{2} - 24 z}{3 z^{2} \cdot (12 z)}$

Step 1

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

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Step 1.1

Move $z$ .

$\frac{3 z^{2} - 24 z}{3 (z \cdot z^{2}) \cdot 12}$

Step 1.2

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

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Step 1.2.1

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

$\frac{3 z^{2} - 24 z}{3 (z^{1} z^{2}) \cdot 12}$

Step 1.2.2

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

$\frac{3 z^{2} - 24 z}{3 z^{1 + 2} \cdot 12}$

$\frac{3 z^{2} - 24 z}{3 z^{1 + 2} \cdot 12}$

Step 1.3

Add $1$ and $2$ .

$\frac{3 z^{2} - 24 z}{3 z^{3} \cdot 12}$

$\frac{3 z^{2} - 24 z}{3 z^{3} \cdot 12}$

Step 2

Factor $3 z$ out of $3 z^{2} - 24 z$ .

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Step 2.1

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

$\frac{3 z (z) - 24 z}{3 z^{3} \cdot 12}$

Step 2.2

Factor $3 z$ out of $- 24 z$ .

$\frac{3 z (z) + 3 z (- 8)}{3 z^{3} \cdot 12}$

Step 2.3

Factor $3 z$ out of $3 z (z) + 3 z (- 8)$ .

$\frac{3 z (z - 8)}{3 z^{3} \cdot 12}$

$\frac{3 z (z - 8)}{3 z^{3} \cdot 12}$

Step 3

Multiply $12$ by $3$ .

$\frac{3 z (z - 8)}{36 z^{3}}$

Step 4

Cancel the common factor of $3$ and $36$ .

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Step 4.1

Factor $3$ out of $3 z (z - 8)$ .

$\frac{3 (z (z - 8))}{36 z^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $36 z^{3}$ .

$\frac{3 (z (z - 8))}{3 (12 z^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (z (z - 8))}{3 (12 z^{3})}$

Step 4.2.3

Rewrite the expression.

$\frac{z (z - 8)}{12 z^{3}}$

$\frac{z (z - 8)}{12 z^{3}}$

$\frac{z (z - 8)}{12 z^{3}}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $z$ out of $12 z^{3}$ .

$\frac{z (z - 8)}{z (12 z^{2})}$

Step 5.2

Cancel the common factor.

$\frac{z (z - 8)}{z (12 z^{2})}$

Step 5.3

Rewrite the expression.

$\frac{z - 8}{12 z^{2}}$

$\frac{z - 8}{12 z^{2}}$

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