Simplify ((3^3)^2+(3^2)^3+3^2*3^4)/9

$\frac{{(3^{3})}^{2} + {(3^{2})}^{3} + 3^{2} \cdot 3^{4}}{9}$

Simplify the numerator.

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

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

$\frac{3^{3 \cdot 2} + {(3^{2})}^{3} + 3^{2} \cdot 3^{4}}{9}$

Multiply $3$ by $2$ .

$\frac{3^{6} + {(3^{2})}^{3} + 3^{2} \cdot 3^{4}}{9}$

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

$\frac{729 + {(3^{2})}^{3} + 3^{2} \cdot 3^{4}}{9}$

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

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

$\frac{729 + 3^{2 \cdot 3} + 3^{2} \cdot 3^{4}}{9}$

Multiply $2$ by $3$ .

$\frac{729 + 3^{6} + 3^{2} \cdot 3^{4}}{9}$

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

$\frac{729 + 729 + 3^{2} \cdot 3^{4}}{9}$

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

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

$\frac{729 + 729 + 3^{2 + 4}}{9}$

Add $2$ and $4$ .

$\frac{729 + 729 + 3^{6}}{9}$

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

$\frac{729 + 729 + 729}{9}$

Add $729$ and $729$ .

$\frac{1458 + 729}{9}$

Add $1458$ and $729$ .

$\frac{2187}{9}$

Divide $2187$ by $9$ .

$243$