Finite Math Examples

$\sqrt{9 e^{4}} \cdot (2 e^{- 3})$

Step 1

Rewrite $9 e^{4}$ as ${(3 e^{2})}^{2}$ .

$\sqrt{{(3 e^{2})}^{2}} \cdot (2 e^{- 3})$

Step 2

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

$3 e^{2} \cdot (2 e^{- 3})$

Step 3

Multiply $e^{2}$ by $e^{- 3}$ by adding the exponents.

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Step 3.1

Move $e^{- 3}$ .

$3 (e^{- 3} e^{2}) \cdot 2$

Step 3.2

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

$3 e^{- 3 + 2} \cdot 2$

Step 3.3

Add $- 3$ and $2$ .

$3 e^{- 1} \cdot 2$

Step 4

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

$3 \frac{1}{e} \cdot 2$

Step 5

Combine $3$ and $\frac{1}{e}$ .

$\frac{3}{e} \cdot 2$

Step 6

Multiply $\frac{3}{e} \cdot 2$ .

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Step 6.1

Combine $\frac{3}{e}$ and $2$ .

$\frac{3 \cdot 2}{e}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{6}{e}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{e}$

Decimal Form:

$2.20727664 \dots$