Finite Math Examples

${(\frac{7 x - 2}{x \sqrt{y}})}^{2}$

Step 1

Multiply $\frac{7 x - 2}{x \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

${(\frac{7 x - 2}{x \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}})}^{2}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{7 x - 2}{x \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

${(\frac{(7 x - 2) \sqrt{y}}{x \sqrt{y} \sqrt{y}})}^{2}$

Step 2.2

Move $\sqrt{y}$ .

${(\frac{(7 x - 2) \sqrt{y}}{x (\sqrt{y} \sqrt{y})})}^{2}$

Step 2.3

Raise $\sqrt{y}$ to the power of $1$ .

${(\frac{(7 x - 2) \sqrt{y}}{x ({\sqrt{y}}^{1} \sqrt{y})})}^{2}$

Step 2.4

Raise $\sqrt{y}$ to the power of $1$ .

${(\frac{(7 x - 2) \sqrt{y}}{x ({\sqrt{y}}^{1} {\sqrt{y}}^{1})})}^{2}$

Step 2.5

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

${(\frac{(7 x - 2) \sqrt{y}}{x {\sqrt{y}}^{1 + 1}})}^{2}$

Step 2.6

Add $1$ and $1$ .

${(\frac{(7 x - 2) \sqrt{y}}{x {\sqrt{y}}^{2}})}^{2}$

Step 2.7

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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Step 2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

${(\frac{(7 x - 2) \sqrt{y}}{x {(y^{\frac{1}{2}})}^{2}})}^{2}$

Step 2.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{(7 x - 2) \sqrt{y}}{x y^{\frac{1}{2} \cdot 2}})}^{2}$

Step 2.7.3

Combine $\frac{1}{2}$ and $2$ .

${(\frac{(7 x - 2) \sqrt{y}}{x y^{\frac{2}{2}}})}^{2}$

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

${(\frac{(7 x - 2) \sqrt{y}}{x y^{\frac{2}{2}}})}^{2}$

Step 2.7.4.2

Rewrite the expression.

${(\frac{(7 x - 2) \sqrt{y}}{x y^{1}})}^{2}$

Step 2.7.5

Simplify.

${(\frac{(7 x - 2) \sqrt{y}}{x y})}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $\frac{(7 x - 2) \sqrt{y}}{x y}$ .

$\frac{{((7 x - 2) \sqrt{y})}^{2}}{{(x y)}^{2}}$

Step 3.2

Apply the product rule to $(7 x - 2) \sqrt{y}$ .

$\frac{{(7 x - 2)}^{2} {\sqrt{y}}^{2}}{{(x y)}^{2}}$

Step 3.3

Apply the product rule to $x y$ .

$\frac{{(7 x - 2)}^{2} {\sqrt{y}}^{2}}{x^{2} y^{2}}$

Step 4

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{{(7 x - 2)}^{2} {(y^{\frac{1}{2}})}^{2}}{x^{2} y^{2}}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{{(7 x - 2)}^{2} y^{\frac{1}{2} \cdot 2}}{x^{2} y^{2}}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{{(7 x - 2)}^{2} y^{\frac{2}{2}}}{x^{2} y^{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{{(7 x - 2)}^{2} y^{\frac{2}{2}}}{x^{2} y^{2}}$

Step 4.4.2

Rewrite the expression.

$\frac{{(7 x - 2)}^{2} y^{1}}{x^{2} y^{2}}$

Step 4.5

Simplify.

$\frac{{(7 x - 2)}^{2} y}{x^{2} y^{2}}$

Step 5

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

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Step 5.1

Factor $y$ out of ${(7 x - 2)}^{2} y$ .

$\frac{y {(7 x - 2)}^{2}}{x^{2} y^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{y {(7 x - 2)}^{2}}{y (x^{2} y)}$

Step 5.2.2

Cancel the common factor.

$\frac{y {(7 x - 2)}^{2}}{y (x^{2} y)}$

Step 5.2.3

Rewrite the expression.

$\frac{{(7 x - 2)}^{2}}{x^{2} y}$