Algebra Examples

$\frac{z^{8} \cdot z^{2}}{z^{5}}$

Step 1

Multiply $z^{8}$ by $z^{2}$ by adding the exponents.

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Step 1.1

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

$\frac{z^{8 + 2}}{z^{5}}$

Step 1.2

Add $8$ and $2$ .

$\frac{z^{10}}{z^{5}}$

Step 2

Cancel the common factor of $z^{10}$ and $z^{5}$ .

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Step 2.1

Factor $z^{5}$ out of $z^{10}$ .

$\frac{z^{5} z^{5}}{z^{5}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{z^{5} z^{5}}{z^{5} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{z^{5} z^{5}}{z^{5} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{z^{5}}{1}$

Step 2.2.4

Divide $z^{5}$ by $1$ .

$z^{5}$