Simplify (81^(1/2)-9^(1/2))^2

${(81^{\frac{1}{2}} - 9^{\frac{1}{2}})}^{2}$

Simplify each term.

Rewrite $81$ as $9^{2}$ .

${({(9^{2})}^{\frac{1}{2}} - 9^{\frac{1}{2}})}^{2}$

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

${(9^{2 (\frac{1}{2})} - 9^{\frac{1}{2}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9^{2 (\frac{1}{2})} - 9^{\frac{1}{2}})}^{2}$

Rewrite the expression.

${(9^{1} - 9^{\frac{1}{2}})}^{2}$

Evaluate the exponent.

${(9 - 9^{\frac{1}{2}})}^{2}$

Rewrite $9$ as $3^{2}$ .

${(9 - {(3^{2})}^{\frac{1}{2}})}^{2}$

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

${(9 - 3^{2 (\frac{1}{2})})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(9 - 3^{2 (\frac{1}{2})})}^{2}$

Rewrite the expression.

${(9 - 3^{1})}^{2}$

Evaluate the exponent.

${(9 - 1 \cdot 3)}^{2}$

Multiply $- 1$ by $3$ .

${(9 - 3)}^{2}$

Simplify the expression.

Subtract $3$ from $9$ .

$6^{2}$

Raise $6$ to the power of $2$ .

$36$