# How do you simplify root3(54e^9x)?

May 6, 2018

Answer = $3. {e}^{3.} \sqrt[3]{2 x}$

#### Explanation:

One of the simplest way is to find the multiples of 54.

$54 = 3 \times 3 \times 3 \times 2$
Now $\sqrt[3]{54} = \sqrt[3]{3 \times 3 \times 3 \times 2}$
$\sqrt[3]{54} = \sqrt[3]{{3}^{3} \times 2}$
$\sqrt[3]{54} = 3. \sqrt[3]{2}$ ------> $\sqrt[3]{{3}^{3}} = 3$

So now we go back to the original question:

$\sqrt[3]{54 {e}^{9} x}$
We simply as follows:
$\sqrt[3]{54} \times {\sqrt[3]{e}}^{9} \times \sqrt[3]{x}$
$\sqrt[3]{54} = 3. \sqrt[3]{2} \times {e}^{9 \times \frac{1}{3}} \times \sqrt[3]{x}$
$\sqrt[3]{54} = 3. \sqrt[3]{2} \times {e}^{3} \times \sqrt[3]{x}$
$3. {e}^{3.} \sqrt[3]{2 x}$