Basic Math Examples

$\frac{5 z^{4}}{y^{5}} \div \frac{8 z^{4} y^{5}}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 z^{4}}{y^{5}} \cdot \frac{3}{8 z^{4} y^{5}}$

Step 2

Combine.

$\frac{5 z^{4} \cdot 3}{y^{5} (8 z^{4} y^{5})}$

Step 3

Multiply $y^{5}$ by $y^{5}$ by adding the exponents.

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Step 3.1

Move $y^{5}$ .

$\frac{5 z^{4} \cdot 3}{y^{5} y^{5} (8 z^{4})}$

Step 3.2

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

$\frac{5 z^{4} \cdot 3}{y^{5 + 5} (8 z^{4})}$

Step 3.3

Add $5$ and $5$ .

$\frac{5 z^{4} \cdot 3}{y^{10} (8 z^{4})}$

Step 4

Cancel the common factor of $z^{4}$ .

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Step 4.1

Cancel the common factor.

$\frac{5 z^{4} \cdot 3}{y^{10} (8 z^{4})}$

Step 4.2

Rewrite the expression.

$\frac{5 \cdot 3}{y^{10} \cdot (8)}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $5$ by $3$ .

$\frac{15}{y^{10} \cdot 8}$

Step 5.2

Move $8$ to the left of $y^{10}$ .

$\frac{15}{8 y^{10}}$