Basic Math Examples

$\frac{8 y^{2} z}{4 y^{4} z^{- 3}}$

Step 1

Move $z^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{8 y^{2} z \cdot z^{3}}{4 y^{4}}$

Step 2

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

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Step 2.1

Move $z^{3}$ .

$\frac{8 y^{2} (z^{3} z)}{4 y^{4}}$

Step 2.2

Multiply $z^{3}$ by $z$ .

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Step 2.2.1

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

$\frac{8 y^{2} (z^{3} z^{1})}{4 y^{4}}$

Step 2.2.2

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

$\frac{8 y^{2} z^{3 + 1}}{4 y^{4}}$

Step 2.3

Add $3$ and $1$ .

$\frac{8 y^{2} z^{4}}{4 y^{4}}$

Step 3

Cancel the common factor of $8$ and $4$ .

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Step 3.1

Factor $4$ out of $8 y^{2} z^{4}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $4 y^{4}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{2 y^{2} z^{4}}{y^{4}}$

Step 4

Cancel the common factor of $y^{2}$ and $y^{4}$ .

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Step 4.1

Factor $y^{2}$ out of $2 y^{2} z^{4}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $y^{4}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{2 z^{4}}{y^{2}}$