Basic Math Examples

$\frac{\frac{6 a}{y^{2}}}{\frac{3 y}{5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 a}{y^{2}} \cdot \frac{5}{3 y}$

Step 2

Combine.

$\frac{6 a \cdot 5}{y^{2} (3 y)}$

Step 3

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

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Step 3.1

Move $y$ .

$\frac{6 a \cdot 5}{y \cdot y^{2} \cdot 3}$

Step 3.2

Multiply $y$ by $y^{2}$ .

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Step 3.2.1

Raise $y$ to the power of $1$ .

$\frac{6 a \cdot 5}{y^{1} y^{2} \cdot 3}$

Step 3.2.2

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

$\frac{6 a \cdot 5}{y^{1 + 2} \cdot 3}$

Step 3.3

Add $1$ and $2$ .

$\frac{6 a \cdot 5}{y^{3} \cdot 3}$

Step 4

Cancel the common factor of $6$ and $3$ .

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Step 4.1

Factor $3$ out of $6 a \cdot 5$ .

$\frac{3 (2 a \cdot 5)}{y^{3} \cdot 3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $y^{3} \cdot 3$ .

$\frac{3 (2 a \cdot 5)}{3 \cdot y^{3}}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (2 a \cdot 5)}{3 \cdot y^{3}}$

Step 4.2.3

Rewrite the expression.

$\frac{2 a \cdot 5}{y^{3}}$

Step 5

Multiply $5$ by $2$ .

$\frac{10 a}{y^{3}}$