Basic Math Examples

$\sqrt{4 e^{4}} \cdot \sqrt[3]{8 e^{12}}$

Step 1

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

$\sqrt{{(2 e^{2})}^{2}} \cdot \sqrt[3]{8 e^{12}}$

Step 2

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

$2 e^{2} \cdot \sqrt[3]{8 e^{12}}$

Step 3

Rewrite $8 e^{12}$ as ${(2 e^{4})}^{3}$ .

$2 e^{2} \cdot \sqrt[3]{{(2 e^{4})}^{3}}$

Step 4

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

$2 e^{2} \cdot (2 e^{4})$

Step 5

Multiply $e^{2}$ by $e^{4}$ by adding the exponents.

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Step 5.1

Move $e^{4}$ .

$2 (e^{4} e^{2}) \cdot 2$

Step 5.2

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

$2 e^{4 + 2} \cdot 2$

Step 5.3

Add $4$ and $2$ .

$2 e^{6} \cdot 2$

Step 6

Multiply $2$ by $2$ .

$4 e^{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$4 e^{6}$

Decimal Form:

$1613.71517397 \dots$