Simplify (2/(3^(-3/2)))^(1/3)

${(\frac{2}{3^{\frac{- 3}{2}}})}^{\frac{1}{3}}$

Move $3^{\frac{- 3}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(2 \cdot 3^{- \frac{- 3}{2}})}^{\frac{1}{3}}$

Move the negative in front of the fraction.

${(2 \cdot 3^{- - \frac{3}{2}})}^{\frac{1}{3}}$

Multiply $- - \frac{3}{2}$ .

Multiply $- 1$ by $- 1$ .

${(2 \cdot 3^{1 (\frac{3}{2})})}^{\frac{1}{3}}$

Multiply $\frac{3}{2}$ by $1$ .

${(2 \cdot 3^{\frac{3}{2}})}^{\frac{1}{3}}$

Apply the product rule to $2 \cdot 3^{\frac{3}{2}}$ .

$2^{\frac{1}{3}} \cdot {(3^{\frac{3}{2}})}^{\frac{1}{3}}$

Multiply the exponents in ${(3^{\frac{3}{2}})}^{\frac{1}{3}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.18224727 \dots$