Finite Math Examples

$300000 e^{- 0.09 \cdot 7 + \sqrt{\frac{7}{2}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 0.09$ by $7$ .

$300000 e^{- 0.63 + \sqrt{\frac{7}{2}}}$

Step 1.2

Rewrite $\sqrt{\frac{7}{2}}$ as $\frac{\sqrt{7}}{\sqrt{2}}$ .

$300000 e^{- 0.63 + \frac{\sqrt{7}}{\sqrt{2}}}$

Step 1.3

Multiply $\frac{\sqrt{7}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$300000 e^{- 0.63 + \frac{\sqrt{7}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}}$

Step 1.4

Combine and simplify the denominator.

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Step 1.4.1

Multiply $\frac{\sqrt{7}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{\sqrt{2} \sqrt{2}}}$

Step 1.4.2

Raise $\sqrt{2}$ to the power of $1$ .

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}}$

Step 1.4.3

Raise $\sqrt{2}$ to the power of $1$ .

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}}$

Step 1.4.4

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

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}}$

Step 1.4.5

Add $1$ and $1$ .

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{{\sqrt{2}}^{2}}}$

Step 1.4.6

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

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Step 1.4.6.1

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

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}}$

Step 1.4.6.2

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

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}}$

Step 1.4.6.3

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

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{2^{\frac{2}{2}}}}$

Step 1.4.6.4

Cancel the common factor of $2$ .

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Step 1.4.6.4.1

Cancel the common factor.

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{2^{\frac{2}{2}}}}$

Step 1.4.6.4.2

Rewrite the expression.

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{2^{1}}}$

Step 1.4.6.5

Evaluate the exponent.

$300000 e^{- 0.63 + \frac{\sqrt{7} \sqrt{2}}{2}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Combine using the product rule for radicals.

$300000 e^{- 0.63 + \frac{\sqrt{7 \cdot 2}}{2}}$

Step 1.5.2

Multiply $7$ by $2$ .

$300000 e^{- 0.63 + \frac{\sqrt{14}}{2}}$

Step 2

To write $- 0.63$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$300000 e^{- 0.63 \cdot \frac{2}{2} + \frac{\sqrt{14}}{2}}$

Step 3

Combine $- 0.63$ and $\frac{2}{2}$ .

$300000 e^{\frac{- 0.63 \cdot 2}{2} + \frac{\sqrt{14}}{2}}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$300000 e^{\frac{- 0.63 \cdot 2 + \sqrt{14}}{2}}$

Step 4.2

Multiply $- 0.63$ by $2$ .

$300000 e^{\frac{- 1.26 + \sqrt{14}}{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$300000 e^{\frac{- 1.26 + \sqrt{14}}{2}}$

Decimal Form:

$1037543.48869743$