Simplify (11^(3/2)*11^(-5/2))^(-1/3)

${(11^{\frac{3}{2}} \cdot 11^{- \frac{5}{2}})}^{- \frac{1}{3}}$

Multiply $11^{\frac{3}{2}}$ by $11^{- \frac{5}{2}}$ by adding the exponents.

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

${(11^{\frac{3}{2} - \frac{5}{2}})}^{- \frac{1}{3}}$

Combine the numerators over the common denominator.

${(11^{\frac{3 - 5}{2}})}^{- \frac{1}{3}}$

Subtract $5$ from $3$ .

${(11^{\frac{- 2}{2}})}^{- \frac{1}{3}}$

Divide $- 2$ by $2$ .

${(11^{- 1})}^{- \frac{1}{3}}$

Multiply the exponents in ${(11^{- 1})}^{- \frac{1}{3}}$ .

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

$11^{- - \frac{1}{3}}$

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

$11^{1 (\frac{1}{3})}$

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

$11^{\frac{1}{3}}$

The result can be shown in multiple forms.

Exact Form:

$11^{\frac{1}{3}}$

Decimal Form:

$2.22398009 \dots$