Finite Math Examples

$0 = y^{4} e^{x}$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $y^{4} e^{x} = 0$ .

$y^{4} e^{x} = 0$

Step 1.2

Divide each term in $y^{4} e^{x} = 0$ by $e^{x}$ and simplify.

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Step 1.2.1

Divide each term in $y^{4} e^{x} = 0$ by $e^{x}$ .

$\frac{y^{4} e^{x}}{e^{x}} = \frac{0}{e^{x}}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

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

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{y^{4} e^{x}}{e^{x}} = \frac{0}{e^{x}}$

Step 1.2.2.1.2

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

$y^{4} = \frac{0}{e^{x}}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $0$ by $e^{x}$ .

$y^{4} = 0$

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

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

$y = \pm 0$

Step 1.4.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 2

Set $y^{4} e^{x}$ equal to $0$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true