Basic Math Examples

$\frac{8 y z^{- 2}}{2 y^{- 6} z^{5}}$

Step 1

Move $z^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{8 y}{2 y^{- 6} z^{5} z^{2}}$

Step 2

Multiply $z^{5}$ by $z^{2}$ by adding the exponents.

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Step 2.1

Move $z^{2}$ .

$\frac{8 y}{2 y^{- 6} (z^{2} z^{5})}$

Step 2.2

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

$\frac{8 y}{2 y^{- 6} z^{2 + 5}}$

Step 2.3

Add $2$ and $5$ .

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

Step 3

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

Multiply $y$ by $y^{6}$ by adding the exponents.

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Step 4.1

Move $y^{6}$ .

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

Step 4.2

Multiply $y^{6}$ by $y$ .

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Step 4.2.1

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

$\frac{8 (y^{6} y^{1})}{2 z^{7}}$

Step 4.2.2

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

$\frac{8 y^{6 + 1}}{2 z^{7}}$

Step 4.3

Add $6$ and $1$ .

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

Step 5

Cancel the common factor of $8$ and $2$ .

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Step 5.1

Factor $2$ out of $8 y^{7}$ .

$\frac{2 (4 y^{7})}{2 z^{7}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 z^{7}$ .

$\frac{2 (4 y^{7})}{2 (z^{7})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (4 y^{7})}{2 z^{7}}$

Step 5.2.3

Rewrite the expression.

$\frac{4 y^{7}}{z^{7}}$