Basic Math Examples

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

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

Step 1

Rewrite

4 e^{4}

$4 e^{4}$ as

{(2 e^{2})}^{2}

${(2 e^{2})}^{2}$ .

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

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

Step 2

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

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

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

Step 3

Rewrite

8 e^{12}

$8 e^{12}$ as

{(2 e^{4})}^{3}

${(2 e^{4})}^{3}$ .

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

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

Step 5

Multiply

e^{2}

$e^{2}$ by

e^{4}

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

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Step 5.1

Move

e^{4}

$e^{4}$ .

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

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

Step 5.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

2 e^{4 + 2} \cdot 2

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

Step 5.3

Add

4

$4$ and

2

$2$ .

2 e^{6} \cdot 2

$2 e^{6} \cdot 2$

2 e^{6} \cdot 2

$2 e^{6} \cdot 2$

Step 6

Multiply

2

$2$ by

2

$2$ .

4 e^{6}

$4 e^{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

4 e^{6}

$4 e^{6}$

Decimal Form:

1613.71517397 \dots

$1613.71517397 \dots$