Simplify square root of (4(27e^13x))/(3e^7x^-3)

$\sqrt{\frac{4 (27 e^{13} x)}{3 e^{7} x^{- 3}}}$

Multiply $4$ by $27$ .

$\sqrt{\frac{108 e^{13} x}{3 e^{7} x^{- 3}}}$

Reduce the expression $\frac{108 e^{13} x}{3 e^{7} x^{- 3}}$ by cancelling the common factors.

Factor $3$ out of $108 e^{13} x$ .

$\sqrt{\frac{3 (36 e^{13} x)}{3 e^{7} x^{- 3}}}$

Factor $3$ out of $3 e^{7} x^{- 3}$ .

$\sqrt{\frac{3 (36 e^{13} x)}{3 (e^{7} x^{- 3})}}$

Cancel the common factor.

$\sqrt{\frac{3 (36 e^{13} x)}{3 (e^{7} x^{- 3})}}$

Rewrite the expression.

$\sqrt{\frac{36 e^{13} x}{e^{7} x^{- 3}}}$

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt{\frac{36 e^{13} x \cdot x^{3}}{e^{7}}}$

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\sqrt{\frac{36 e^{13} (x^{3} x)}{e^{7}}}$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$\sqrt{\frac{36 e^{13} (x^{3} x^{1})}{e^{7}}}$

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

$\sqrt{\frac{36 e^{13} x^{3 + 1}}{e^{7}}}$

Add $3$ and $1$ .

$\sqrt{\frac{36 e^{13} x^{4}}{e^{7}}}$

Cancel the common factor of $e^{13}$ and $e^{7}$ .

Factor $e^{7}$ out of $36 e^{13} x^{4}$ .

$\sqrt{\frac{e^{7} (36 e^{6} x^{4})}{e^{7}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{e^{7} (36 e^{6} x^{4})}{e^{7} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{e^{7} (36 e^{6} x^{4})}{e^{7} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{36 e^{6} x^{4}}{1}}$

Divide $36 e^{6} x^{4}$ by $1$ .

$\sqrt{36 e^{6} x^{4}}$

Rewrite $36 e^{6} x^{4}$ as ${(6 e^{3} x^{2})}^{2}$ .

$\sqrt{{(6 e^{3} x^{2})}^{2}}$

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

$6 e^{3} x^{2}$