Basic Math Examples

$\frac{6 z^{2} y^{4}}{2 z^{- 3} y^{- 2}}$

Step 1

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

$\frac{6 z^{2} y^{4} z^{3}}{2 y^{- 2}}$

Step 2

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

$\frac{6 z^{2} y^{4} z^{3} y^{2}}{2}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $z^{2}$ by $z^{3}$ by adding the exponents.

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Step 3.1.1

Move $z^{3}$ .

$\frac{6 (z^{3} z^{2}) y^{4} y^{2}}{2}$

Step 3.1.2

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

$\frac{6 z^{3 + 2} y^{4} y^{2}}{2}$

Step 3.1.3

Add $3$ and $2$ .

$\frac{6 z^{5} y^{4} y^{2}}{2}$

Step 3.2

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

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Step 3.2.1

Move $y^{2}$ .

$\frac{6 z^{5} (y^{2} y^{4})}{2}$

Step 3.2.2

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

$\frac{6 z^{5} y^{2 + 4}}{2}$

Step 3.2.3

Add $2$ and $4$ .

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

Step 4

Cancel the common factor of $6$ and $2$ .

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Step 4.1

Factor $2$ out of $6 z^{5} y^{6}$ .

$\frac{2 (3 z^{5} y^{6})}{2}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 z^{5} y^{6})}{2 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (3 z^{5} y^{6})}{2 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{3 z^{5} y^{6}}{1}$

Step 4.2.4

Divide $3 z^{5} y^{6}$ by $1$ .

$3 z^{5} y^{6}$