Pre-Algebra Examples

$\frac{3 x^{3}}{6 y^{5}} \div \frac{x^{5} y}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y^{5}$ .

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Step 3.2.1

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

$\frac{3 x^{3} \cdot 3}{6 (y^{1} y^{5}) x^{5}}$

Step 3.2.2

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

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

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

Step 3.3

Add $1$ and $5$ .

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $6 y^{6} x^{5}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $x^{3}$ and $x^{5}$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x^{3}$ out of $2 y^{6} x^{5}$ .

$\frac{x^{3} (3)}{x^{3} (2 y^{6} x^{2})}$

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{3}{2 y^{6} x^{2}}$

$\frac{3}{2 y^{6} x^{2}}$

$\frac{3}{2 y^{6} x^{2}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$