Finite Math Examples

$\frac{x^{2}}{y^{\frac{1}{2}}} = n$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y^{\frac{1}{2}}, 1$

Step 1.2

The LCM of one and any expression is the expression.

$y^{\frac{1}{2}}$

Step 2

Multiply each term in $\frac{x^{2}}{y^{\frac{1}{2}}} = n$ by $y^{\frac{1}{2}}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x^{2}}{y^{\frac{1}{2}}} = n$ by $y^{\frac{1}{2}}$ .

$\frac{x^{2}}{y^{\frac{1}{2}}} y^{\frac{1}{2}} = n y^{\frac{1}{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $y^{\frac{1}{2}}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x^{2}}{y^{\frac{1}{2}}} y^{\frac{1}{2}} = n y^{\frac{1}{2}}$

Step 2.2.1.2

Rewrite the expression.

$x^{2} = n y^{\frac{1}{2}}$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $n y^{\frac{1}{2}} = x^{2}$ .

$n y^{\frac{1}{2}} = x^{2}$

Step 3.2

Divide each term in $n y^{\frac{1}{2}} = x^{2}$ by $n$ and simplify.

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Step 3.2.1

Divide each term in $n y^{\frac{1}{2}} = x^{2}$ by $n$ .

$\frac{n y^{\frac{1}{2}}}{n} = \frac{x^{2}}{n}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor.

$\frac{n y^{\frac{1}{2}}}{n} = \frac{x^{2}}{n}$

Step 3.2.2.2

Divide $y^{\frac{1}{2}}$ by $1$ .

$y^{\frac{1}{2}} = \frac{x^{2}}{n}$

Step 3.3

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(y^{\frac{1}{2}})}^{2} = {(\frac{x^{2}}{n})}^{2}$

Step 3.4

Simplify the exponent.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify ${(y^{\frac{1}{2}})}^{2}$ .

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Step 3.4.1.1.1

Multiply the exponents in ${(y^{\frac{1}{2}})}^{2}$ .

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Step 3.4.1.1.1.1

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

$y^{\frac{1}{2} \cdot 2} = {(\frac{x^{2}}{n})}^{2}$

Step 3.4.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.4.1.1.1.2.1

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = {(\frac{x^{2}}{n})}^{2}$

Step 3.4.1.1.1.2.2

Rewrite the expression.

$y^{1} = {(\frac{x^{2}}{n})}^{2}$

Step 3.4.1.1.2

Simplify.

$y = {(\frac{x^{2}}{n})}^{2}$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify ${(\frac{x^{2}}{n})}^{2}$ .

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Step 3.4.2.1.1

Apply the product rule to $\frac{x^{2}}{n}$ .

$y = \frac{{(x^{2})}^{2}}{n^{2}}$

Step 3.4.2.1.2

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 3.4.2.1.2.1

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

$y = \frac{x^{2 \cdot 2}}{n^{2}}$

Step 3.4.2.1.2.2

Multiply $2$ by $2$ .

$y = \frac{x^{4}}{n^{2}}$