Basic Math Examples

\frac{y^{2}}{2} \div \frac{4}{y} \cdot \frac{y^{2}}{8}

$\frac{y^{2}}{2} \div \frac{4}{y} \cdot \frac{y^{2}}{8}$

Step 1

Combine.

$\frac{\frac{y^{2}}{2} y^{2}}{\frac{4}{y} \cdot 8}$

Step 2

Combine

$\frac{y^{2}}{2}$ and

$y^{2}$ .

$\frac{\frac{y^{2} y^{2}}{2}}{\frac{4}{y} \cdot 8}$

Step 3

Combine

$\frac{4}{y}$ and

$8$ .

$\frac{\frac{y^{2} y^{2}}{2}}{\frac{4 \cdot 8}{y}}$

Step 4

Multiply

$y^{2}$ by

$y^{2}$ by adding the exponents.

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Step 4.1

Use the power rule

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

$\frac{\frac{y^{2 + 2}}{2}}{\frac{4 \cdot 8}{y}}$

Step 4.2

Add

$2$ and

$2$ .

$\frac{\frac{y^{4}}{2}}{\frac{4 \cdot 8}{y}}$

Step 5

Multiply

$4$ by

$8$ .

$\frac{\frac{y^{4}}{2}}{\frac{32}{y}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{4}}{2} \cdot \frac{y}{32}$

Step 7

Combine.

$\frac{y^{4} y}{2 \cdot 32}$

Step 8

Multiply

$y^{4}$ by

$y$ by adding the exponents.

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Step 8.1

Multiply

$y^{4}$ by

$y$ .

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Step 8.1.1

Raise

$y$ to the power of

$1$ .

$\frac{y^{4} y^{1}}{2 \cdot 32}$

Step 8.1.2

Use the power rule

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

$\frac{y^{4 + 1}}{2 \cdot 32}$

Step 8.2

Add

$4$ and

$1$ .

$\frac{y^{5}}{2 \cdot 32}$

Step 9

Multiply

$2$ by

$32$ .

$\frac{y^{5}}{64}$