Linear Algebra Examples

$\frac{\sqrt[3]{5^{- 1}}}{\frac{60}{y^{2}}}$

Step 1

Set the denominator in $\frac{60}{y^{2}}$ equal to $0$ to find where the expression is undefined.

$y^{2} = 0$

Step 2

Solve for $y$ .

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Step 2.1

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

$y = \pm \sqrt{0}$

Step 2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.1

Rewrite $0$ as $0^{2}$ .

$y = \pm \sqrt{0^{2}}$

Step 2.2.2

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

$y = \pm 0$

Step 2.2.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 3

Set the denominator in $\frac{\sqrt[3]{5^{- 1}}}{\frac{60}{y^{2}}}$ equal to $0$ to find where the expression is undefined.

$\frac{60}{y^{2}} = 0$

Step 4

Solve for $y$ .

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Step 4.1

Set the numerator equal to zero.

$60 = 0$

Step 4.2

Since $60 \neq 0$ , there are no solutions.

No solution

Step 5

The domain is all values of $y$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${y | y \neq 0}$

Step 6