Simplify 9(3^-2)-(3^4)/(3^2)-( square root of 2^6)÷2

$9 (3^{- 2}) - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 \frac{1}{3^{2}} - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$

Raise $3$ to the power of $2$ .

$9 (\frac{1}{9}) - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$

Cancel the common factor of $9$ .

Cancel the common factor.

$9 (\frac{1}{9}) - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$

Rewrite the expression.

$1 - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}} \div 2$

Cancel the common factor of $3^{4}$ and $3^{2}$ .

Factor $3^{2}$ out of $3^{4}$ .

$1 - \frac{3^{2} \cdot 3^{2}}{3^{2}} - \sqrt{2^{6}} \div 2$

Cancel the common factors.

Multiply by $1$ .

$1 - \frac{3^{2} \cdot 3^{2}}{3^{2} \cdot 1} - \sqrt{2^{6}} \div 2$

Cancel the common factor.

$1 - \frac{3^{2} \cdot 3^{2}}{3^{2} \cdot 1} - \sqrt{2^{6}} \div 2$

Rewrite the expression.

$1 - \frac{3^{2}}{1} - \sqrt{2^{6}} \div 2$

Divide $3^{2}$ by $1$ .

$1 - 3^{2} - \sqrt{2^{6}} \div 2$

Raise $3$ to the power of $2$ .

$1 - 1 \cdot 9 - \sqrt{2^{6}} \div 2$

Multiply $- 1$ by $9$ .

$1 - 9 - \sqrt{2^{6}} \div 2$

Rewrite the division as a fraction.

$1 - 9 - \frac{\sqrt{2^{6}}}{2}$

Simplify the numerator.

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

$1 - 9 - \frac{\sqrt{64}}{2}$

Rewrite $64$ as $8^{2}$ .

$1 - 9 - \frac{\sqrt{8^{2}}}{2}$

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

$1 - 9 - \frac{8}{2}$

Divide $8$ by $2$ .

$1 - 9 - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$1 - 9 - 4$

Simplify by subtracting numbers.

Subtract $9$ from $1$ .

$- 8 - 4$

Subtract $4$ from $- 8$ .

$- 12$