Find the Exact Value 3^-6*((3^4)÷(3^0))^2

$3^{- 6} \cdot {(3^{4} \div 3^{0})}^{2}$

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

$\frac{1}{3^{6}} \cdot {(3^{4} \div 3^{0})}^{2}$

Raise $3$ to the power of $6$ .

$\frac{1}{729} \cdot {(3^{4} \div 3^{0})}^{2}$

Rewrite the division as a fraction.

$\frac{1}{729} \cdot {(\frac{3^{4}}{3^{0}})}^{2}$

Cancel the common factor of $3^{4}$ and $3^{0}$ .

Factor $3^{0}$ out of $3^{4}$ .

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0}})}^{2}$

Cancel the common factors.

Multiply by $1$ .

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0} \cdot 1})}^{2}$

Cancel the common factor.

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0} \cdot 1})}^{2}$

Rewrite the expression.

$\frac{1}{729} \cdot {(\frac{3^{4}}{1})}^{2}$

Divide $3^{4}$ by $1$ .

$\frac{1}{729} \cdot {(3^{4})}^{2}$

Simplify the expression.

Multiply the exponents in ${(3^{4})}^{2}$ .

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

$\frac{1}{729} \cdot 3^{4 \cdot 2}$

Multiply $4$ by $2$ .

$\frac{1}{729} \cdot 3^{8}$

Raise $3$ to the power of $8$ .

$\frac{1}{729} \cdot 6561$

Cancel the common factor of $729$ .

Factor $729$ out of $6561$ .

$\frac{1}{729} \cdot (729 (9))$

Cancel the common factor.

$\frac{1}{729} \cdot (729 \cdot 9)$

Rewrite the expression.

$9$