Finite Math Examples

$e^{3.22}$

Step 1

Convert expressions with fractional exponents to radicals.

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Step 1.1

Change $3.22$ into a fraction.

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Step 1.1.1

Multiply by $\frac{100}{100}$ to remove the decimal.

$e^{\frac{100 \cdot 3.22}{100}}$

Step 1.1.2

Multiply $100$ by $3.22$ .

$e^{\frac{322}{100}}$

Step 1.1.3

Cancel the common factor of $322$ and $100$ .

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Step 1.1.3.1

Factor $2$ out of $322$ .

$e^{\frac{2 (161)}{100}}$

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor $2$ out of $100$ .

$e^{\frac{2 \cdot 161}{2 \cdot 50}}$

Step 1.1.3.2.2

Cancel the common factor.

$e^{\frac{2 \cdot 161}{2 \cdot 50}}$

Step 1.1.3.2.3

Rewrite the expression.

$e^{\frac{161}{50}}$

Step 1.2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[50]{e^{161}}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3