Pre-Algebra Examples

$\frac{\sqrt{125 x^{9} y^{10}}}{\sqrt{5 x^{2} y^{2}}}$

Step 1

Write $\frac{\sqrt{125 x^{9} y^{10}}}{\sqrt{5 x^{2} y^{2}}}$ as an equation.

$\frac{\sqrt{125 x^{9} y^{10}}}{\sqrt{5 x^{2} y^{2}}} = 0$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{\sqrt{125 x^{9} y^{10}}}{\sqrt{5 x^{2} y^{2}}}$ .

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Step 2.2.1.1

Combine $\sqrt{125 x^{9} y^{10}}$ and $\sqrt{5 x^{2} y^{2}}$ into a single radical.

$\sqrt{\frac{125 x^{9} y^{10}}{5 x^{2} y^{2}}} = 0$

Step 2.2.1.2

Reduce the expression $\frac{125 x^{9} y^{10}}{5 x^{2} y^{2}}$ by cancelling the common factors.

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Step 2.2.1.2.1

Factor $5$ out of $125 x^{9} y^{10}$ .

$\sqrt{\frac{5 (25 x^{9} y^{10})}{5 x^{2} y^{2}}} = 0$

Step 2.2.1.2.2

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

$\sqrt{\frac{5 (25 x^{9} y^{10})}{5 (x^{2} y^{2})}} = 0$

Step 2.2.1.2.3

Cancel the common factor.

$\sqrt{\frac{5 (25 x^{9} y^{10})}{5 (x^{2} y^{2})}} = 0$

Step 2.2.1.2.4

Rewrite the expression.

$\sqrt{\frac{25 x^{9} y^{10}}{x^{2} y^{2}}} = 0$

Step 2.2.1.3

Cancel the common factor of $x^{9}$ and $x^{2}$ .

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Step 2.2.1.3.1

Factor $x^{2}$ out of $25 x^{9} y^{10}$ .

$\sqrt{\frac{x^{2} (25 x^{7} y^{10})}{x^{2} y^{2}}} = 0$

Step 2.2.1.3.2

Cancel the common factors.

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Step 2.2.1.3.2.1

Factor $x^{2}$ out of $x^{2} y^{2}$ .

$\sqrt{\frac{x^{2} (25 x^{7} y^{10})}{x^{2} (y^{2})}} = 0$

Step 2.2.1.3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{2} (25 x^{7} y^{10})}{x^{2} y^{2}}} = 0$

Step 2.2.1.3.2.3

Rewrite the expression.

$\sqrt{\frac{25 x^{7} y^{10}}{y^{2}}} = 0$

Step 2.2.1.4

Cancel the common factor of $y^{10}$ and $y^{2}$ .

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Step 2.2.1.4.1

Factor $y^{2}$ out of $25 x^{7} y^{10}$ .

$\sqrt{\frac{y^{2} (25 x^{7} y^{8})}{y^{2}}} = 0$

Step 2.2.1.4.2

Cancel the common factors.

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Step 2.2.1.4.2.1

Multiply by $1$ .

$\sqrt{\frac{y^{2} (25 x^{7} y^{8})}{y^{2} \cdot 1}} = 0$

Step 2.2.1.4.2.2

Cancel the common factor.

$\sqrt{\frac{y^{2} (25 x^{7} y^{8})}{y^{2} \cdot 1}} = 0$

Step 2.2.1.4.2.3

Rewrite the expression.

$\sqrt{\frac{25 x^{7} y^{8}}{1}} = 0$

Step 2.2.1.4.2.4

Divide $25 x^{7} y^{8}$ by $1$ .

$\sqrt{25 x^{7} y^{8}} = 0$

Step 2.2.1.5

Rewrite $25 x^{7} y^{8}$ as ${(5 x^{3} y^{4})}^{2} x$ .

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Step 2.2.1.5.1

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} x^{7} y^{8}} = 0$

Step 2.2.1.5.2

Factor out $x^{6}$ .

$\sqrt{5^{2} (x^{6} x) y^{8}} = 0$

Step 2.2.1.5.3

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{5^{2} ({(x^{3})}^{2} x) y^{8}} = 0$

Step 2.2.1.5.4

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\sqrt{5^{2} ({(x^{3})}^{2} x) {(y^{4})}^{2}} = 0$

Step 2.2.1.5.5

Move $x$ .

$\sqrt{5^{2} ({(x^{3})}^{2}) {(y^{4})}^{2} x} = 0$

Step 2.2.1.5.6

Rewrite $5^{2} ({(x^{3})}^{2}) {(y^{4})}^{2}$ as ${(5 x^{3} y^{4})}^{2}$ .

$\sqrt{{(5 x^{3} y^{4})}^{2} x} = 0$

Step 2.2.1.6

Pull terms out from under the radical.

$5 x^{3} y^{4} \sqrt{x} = 0$

Step 2.3

Divide each term in $5 x^{3} y^{4} \sqrt{x} = 0$ by $5 x^{3} \sqrt{x}$ and simplify.

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Step 2.3.1

Divide each term in $5 x^{3} y^{4} \sqrt{x} = 0$ by $5 x^{3} \sqrt{x}$ .

$\frac{5 x^{3} y^{4} \sqrt{x}}{5 x^{3} \sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x^{3} y^{4} \sqrt{x}}{5 x^{3} \sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2.1.2

Rewrite the expression.

$\frac{x^{3} y^{4} \sqrt{x}}{x^{3} \sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2.2

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

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Step 2.3.2.2.1

Cancel the common factor.

$\frac{x^{3} y^{4} \sqrt{x}}{x^{3} \sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2.2.2

Rewrite the expression.

$\frac{y^{4} \sqrt{x}}{\sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2.3

Cancel the common factor of $\sqrt{x}$ .

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Step 2.3.2.3.1

Cancel the common factor.

$\frac{y^{4} \sqrt{x}}{\sqrt{x}} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.2.3.2

Divide $y^{4}$ by $1$ .

$y^{4} = \frac{0}{5 x^{3} \sqrt{x}}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $0$ and $5$ .

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Step 2.3.3.1.1

Factor $5$ out of $0$ .

$y^{4} = \frac{5 (0)}{5 x^{3} \sqrt{x}}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $5$ out of $5 x^{3} \sqrt{x}$ .

$y^{4} = \frac{5 (0)}{5 (x^{3} \sqrt{x})}$

Step 2.3.3.1.2.2

Cancel the common factor.

$y^{4} = \frac{5 \cdot 0}{5 (x^{3} \sqrt{x})}$

Step 2.3.3.1.2.3

Rewrite the expression.

$y^{4} = \frac{0}{x^{3} \sqrt{x}}$

Step 2.3.3.2

Divide $0$ by $x^{3} \sqrt{x}$ .

$y^{4} = 0$

Step 2.4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt[4]{0}$

Step 2.5

Simplify $\pm \sqrt[4]{0}$ .

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Step 2.5.1

Rewrite $0$ as $0^{4}$ .

$y = \pm \sqrt[4]{0^{4}}$

Step 2.5.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 0$

Step 2.5.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 3

Using the slope-intercept form, the slope is $0$ .

$m = 0$

Step 4