Simplify (3^2*3^-4)^4

${(3^{2} \times 3^{- 4})}^{4}$

Multiply $3^{2}$ by $3^{- 4}$ by adding the exponents.

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

${(3^{2 - 4})}^{4}$

Subtract $4$ from $2$ .

${(3^{- 2})}^{4}$

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

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

$3^{- 2 \cdot 4}$

Multiply $- 2$ by $4$ .

$3^{- 8}$

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

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

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

$\frac{1}{6561}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6561}$

Decimal Form:

$0.00015241 \dots$