Basic Math Examples

$\frac{12 a^{6} \cdot y^{- 2} \cdot z^{3}}{28 a^{- 4} \cdot z^{7} \cdot y^{- 3}}$

Step 1

Move $a^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 a^{6} \cdot y^{- 2} \cdot z^{3} a^{4}}{28 \cdot z^{7} \cdot y^{- 3}}$

Step 2

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

$\frac{12 a^{6} \cdot y^{- 2} \cdot z^{3} a^{4} y^{3}}{28 \cdot z^{7}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $a^{6}$ by $a^{4}$ by adding the exponents.

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Step 3.1.1

Move $a^{4}$ .

$\frac{12 (a^{4} a^{6}) \cdot y^{- 2} \cdot z^{3} y^{3}}{28 \cdot z^{7}}$

Step 3.1.2

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

$\frac{12 a^{4 + 6} \cdot y^{- 2} \cdot z^{3} y^{3}}{28 \cdot z^{7}}$

Step 3.1.3

Add $4$ and $6$ .

$\frac{12 a^{10} \cdot y^{- 2} \cdot z^{3} y^{3}}{28 \cdot z^{7}}$

Step 3.2

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

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Step 3.2.1

Move $y^{3}$ .

$\frac{12 a^{10} \cdot (y^{3} y^{- 2}) \cdot z^{3}}{28 \cdot z^{7}}$

Step 3.2.2

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

$\frac{12 a^{10} \cdot y^{3 - 2} \cdot z^{3}}{28 \cdot z^{7}}$

Step 3.2.3

Subtract $2$ from $3$ .

$\frac{12 a^{10} \cdot y^{1} \cdot z^{3}}{28 \cdot z^{7}}$

Step 3.3

Simplify $12 a^{10} \cdot y^{1} \cdot z^{3}$ .

$\frac{12 a^{10} \cdot y \cdot z^{3}}{28 \cdot z^{7}}$

Step 4

Cancel the common factor of $12$ and $28$ .

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Step 4.1

Factor $4$ out of $12 a^{10} \cdot y \cdot z^{3}$ .

$\frac{4 (3 a^{10} \cdot y \cdot z^{3})}{28 \cdot z^{7}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $28 \cdot z^{7}$ .

$\frac{4 (3 a^{10} \cdot y \cdot z^{3})}{4 (7 \cdot z^{7})}$

Step 4.2.2

Cancel the common factor.

$\frac{4 (3 a^{10} \cdot y \cdot z^{3})}{4 (7 \cdot z^{7})}$

Step 4.2.3

Rewrite the expression.

$\frac{3 a^{10} \cdot y \cdot z^{3}}{7 \cdot z^{7}}$

Step 5

Cancel the common factor of $z^{3}$ and $z^{7}$ .

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Step 5.1

Factor $z^{3}$ out of $3 a^{10} \cdot y \cdot z^{3}$ .

$\frac{z^{3} \cdot (3 a^{10} \cdot y)}{7 \cdot z^{7}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $z^{3}$ out of $7 \cdot z^{7}$ .

$\frac{z^{3} \cdot (3 a^{10} \cdot y)}{z^{3} (7 \cdot z^{4})}$

Step 5.2.2

Cancel the common factor.

$\frac{z^{3} \cdot (3 a^{10} \cdot y)}{z^{3} (7 \cdot z^{4})}$

Step 5.2.3

Rewrite the expression.

$\frac{3 a^{10} \cdot y}{7 \cdot z^{4}}$

$\frac{3 a^{10} y}{7 z^{4}}$