Simplify (11^(4/5)*11^(-4/5))^2

${(11^{\frac{4}{5}} \cdot 11^{- \frac{4}{5}})}^{2}$

Multiply $11^{\frac{4}{5}}$ by $11^{- \frac{4}{5}}$ by adding the exponents.

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

${(11^{\frac{4}{5} - \frac{4}{5}})}^{2}$

Combine the numerators over the common denominator.

${(11^{\frac{4 - 4}{5}})}^{2}$

Subtract $4$ from $4$ .

${(11^{\frac{0}{5}})}^{2}$

Divide $0$ by $5$ .

${(11^{0})}^{2}$

Simplify $11^{0}$ .

$1^{2}$

One to any power is one.

$1$