Basic Math Examples

$θ (150) = 150 e^{- 0.08059 \cdot 15}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.08059$ by $15$ .

$θ (150) = 150 e^{- 1.20885}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$θ (150) = 150 \frac{1}{e^{1.20885}}$

Step 1.3

Combine $150$ and $\frac{1}{e^{1.20885}}$ .

$θ (150) = \frac{150}{e^{1.20885}}$

Step 2

Divide each term in $θ (150) = \frac{150}{e^{1.20885}}$ by $150$ and simplify.

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Step 2.1

Divide each term in $θ (150) = \frac{150}{e^{1.20885}}$ by $150$ .

$\frac{θ (150)}{150} = \frac{\frac{150}{e^{1.20885}}}{150}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $150$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{θ \cdot 150}{150} = \frac{\frac{150}{e^{1.20885}}}{150}$

Step 2.2.1.2

Divide $θ$ by $1$ .

$θ = \frac{\frac{150}{e^{1.20885}}}{150}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$θ = \frac{150}{e^{1.20885}} \cdot \frac{1}{150}$

Step 2.3.2

Combine.

$θ = \frac{150 \cdot 1}{e^{1.20885} \cdot 150}$

Step 2.3.3

Cancel the common factor of $150$ .

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Step 2.3.3.1

Cancel the common factor.

$θ = \frac{150 \cdot 1}{e^{1.20885} \cdot 150}$

Step 2.3.3.2

Rewrite the expression.

$θ = \frac{1}{e^{1.20885}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$θ = \frac{1}{e^{1.20885}}$

Decimal Form:

$θ = 0.29854040 \dots$