Basic Math Examples

$24 y^{3} z^{5} \div 32 y^{2} z^{- 4}$

Step 1

Rewrite the division as a fraction.

$\frac{24 y^{3} z^{5}}{32 y^{2} z^{- 4}}$

Step 2

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

$\frac{24 y^{3} z^{5} z^{4}}{32 y^{2}}$

Step 3

Multiply $z^{5}$ by $z^{4}$ by adding the exponents.

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Step 3.1

Move $z^{4}$ .

$\frac{24 y^{3} (z^{4} z^{5})}{32 y^{2}}$

Step 3.2

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

$\frac{24 y^{3} z^{4 + 5}}{32 y^{2}}$

Step 3.3

Add $4$ and $5$ .

$\frac{24 y^{3} z^{9}}{32 y^{2}}$

Step 4

Cancel the common factor of $24$ and $32$ .

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Step 4.1

Factor $8$ out of $24 y^{3} z^{9}$ .

$\frac{8 (3 y^{3} z^{9})}{32 y^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $8$ out of $32 y^{2}$ .

$\frac{8 (3 y^{3} z^{9})}{8 (4 y^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{8 (3 y^{3} z^{9})}{8 (4 y^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{3 y^{3} z^{9}}{4 y^{2}}$

Step 5

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 5.1

Factor $y^{2}$ out of $3 y^{3} z^{9}$ .

$\frac{y^{2} (3 y z^{9})}{4 y^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{y^{2} (3 y z^{9})}{y^{2} \cdot 4}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{2} (3 y z^{9})}{y^{2} \cdot 4}$

Step 5.2.3

Rewrite the expression.

$\frac{3 y z^{9}}{4}$