Basic Math Examples

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

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

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}}

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

Step 2

Combine.

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

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

Step 3

Multiply

y^{5}

$y^{5}$ by

y^{5}

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

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Step 3.1

Move

y^{5}

$y^{5}$ .

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

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

Step 3.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 3.3

Add

5

$5$ and

5

$5$ .

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

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

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

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

Step 4

Cancel the common factor of

z^{4}

$z^{4}$ .

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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

$y^{10}$ .

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