Algebra Examples

$\frac{22 y^{6} z^{8}}{2 y z^{- 7}}$

Step 1

Move $z^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{22 y^{6} z^{8} z^{7}}{2 y}$

Step 2

Multiply $z^{8}$ by $z^{7}$ by adding the exponents.

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Step 2.1

Move $z^{7}$ .

$\frac{22 y^{6} (z^{7} z^{8})}{2 y}$

Step 2.2

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

$\frac{22 y^{6} z^{7 + 8}}{2 y}$

Step 2.3

Add $7$ and $8$ .

$\frac{22 y^{6} z^{15}}{2 y}$

Step 3

Cancel the common factor of $22$ and $2$ .

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Step 3.1

Factor $2$ out of $22 y^{6} z^{15}$ .

$\frac{2 (11 y^{6} z^{15})}{2 y}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 y$ .

$\frac{2 (11 y^{6} z^{15})}{2 (y)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (11 y^{6} z^{15})}{2 y}$

Step 3.2.3

Rewrite the expression.

$\frac{11 y^{6} z^{15}}{y}$

Step 4

Cancel the common factor of $y^{6}$ and $y$ .

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Step 4.1

Factor $y$ out of $11 y^{6} z^{15}$ .

$\frac{y (11 y^{5} z^{15})}{y}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{y (11 y^{5} z^{15})}{y^{1}}$

Step 4.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (11 y^{5} z^{15})}{y \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{y (11 y^{5} z^{15})}{y \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{11 y^{5} z^{15}}{1}$

Step 4.2.5

Divide $11 y^{5} z^{15}$ by $1$ .

$11 y^{5} z^{15}$