Basic Math Examples

$\frac{y^{5}}{z^{6}} \cdot \frac{z^{2} \cdot c^{- 7}}{y^{2} \cdot c^{9}}$

Step 1

Combine.

$\frac{y^{5} (z^{2} \cdot c^{- 7})}{z^{6} (y^{2} \cdot c^{9})}$

Step 2

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

$\frac{y^{5} z^{2}}{z^{6} (y^{2} \cdot c^{9}) c^{7}}$

Step 3

Multiply $c^{9}$ by $c^{7}$ by adding the exponents.

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Step 3.1

Move $c^{7}$ .

$\frac{y^{5} z^{2}}{z^{6} (y^{2} \cdot (c^{7} c^{9}))}$

Step 3.2

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

$\frac{y^{5} z^{2}}{z^{6} (y^{2} \cdot c^{7 + 9})}$

Step 3.3

Add $7$ and $9$ .

$\frac{y^{5} z^{2}}{z^{6} (y^{2} \cdot c^{16})}$

Step 4

Cancel the common factor of $y^{5}$ and $y^{2}$ .

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Step 4.1

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

$\frac{y^{2} (y^{3} z^{2})}{z^{6} (y^{2} \cdot c^{16})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $z^{6} (y^{2} \cdot c^{16})$ .

$\frac{y^{2} (y^{3} z^{2})}{y^{2} (z^{6} (c^{16}))}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} (y^{3} z^{2})}{y^{2} (z^{6} (c^{16}))}$

Step 4.2.3

Rewrite the expression.

$\frac{y^{3} z^{2}}{z^{6} (c^{16})}$

Step 5

Cancel the common factor of $z^{2}$ and $z^{6}$ .

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Step 5.1

Factor $z^{2}$ out of $y^{3} z^{2}$ .

$\frac{z^{2} y^{3}}{z^{6} (c^{16})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $z^{2}$ out of $z^{6} (c^{16})$ .

$\frac{z^{2} y^{3}}{z^{2} (z^{4} c^{16})}$

Step 5.2.2

Cancel the common factor.

$\frac{z^{2} y^{3}}{z^{2} (z^{4} c^{16})}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{3}}{z^{4} c^{16}}$