Basic Math Examples

$\frac{6 z^{9} \cdot (8 z^{3})}{27 z^{2}}$

Step 1

Multiply $z^{9}$ by $z^{3}$ by adding the exponents.

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Step 1.1

Move $z^{3}$ .

$\frac{6 (z^{3} z^{9}) \cdot 8}{27 z^{2}}$

Step 1.2

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

$\frac{6 z^{3 + 9} \cdot 8}{27 z^{2}}$

Step 1.3

Add $3$ and $9$ .

$\frac{6 z^{12} \cdot 8}{27 z^{2}}$

Step 2

Cancel the common factor of $6$ and $27$ .

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Step 2.1

Factor $3$ out of $6 z^{12} \cdot 8$ .

$\frac{3 (2 z^{12} \cdot 8)}{27 z^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $27 z^{2}$ .

$\frac{3 (2 z^{12} \cdot 8)}{3 (9 z^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (2 z^{12} \cdot 8)}{3 (9 z^{2})}$

Step 2.2.3

Rewrite the expression.

$\frac{2 z^{12} \cdot 8}{9 z^{2}}$

Step 3

Cancel the common factor of $z^{12}$ and $z^{2}$ .

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Step 3.1

Factor $z^{2}$ out of $2 z^{12} \cdot 8$ .

$\frac{z^{2} (2 z^{10} \cdot 8)}{9 z^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $z^{2}$ out of $9 z^{2}$ .

$\frac{z^{2} (2 z^{10} \cdot 8)}{z^{2} \cdot 9}$

Step 3.2.2

Cancel the common factor.

$\frac{z^{2} (2 z^{10} \cdot 8)}{z^{2} \cdot 9}$

Step 3.2.3

Rewrite the expression.

$\frac{2 z^{10} \cdot 8}{9}$

Step 4

Multiply $8$ by $2$ .

$\frac{16 z^{10}}{9}$