Basic Math Examples

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

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 $32$ .

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