Evaluate ((3^2)^3*3^6)/(3^4)

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

Step 1

Cancel the common factor of $3^{6}$ and $3^{4}$ .

Factor $3^{4}$ out of ${(3^{2})}^{3} \cdot 3^{6}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide ${(3^{2})}^{3} \cdot 3^{2}$ by $1$ .

${(3^{2})}^{3} \cdot 3^{2}$

Step 2

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

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

$3^{2 \cdot 3} \cdot 3^{2}$

Multiply $2$ by $3$ .

$3^{6} \cdot 3^{2}$

Step 3

Multiply $3^{6}$ by $3^{2}$ by adding the exponents.

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

$3^{6 + 2}$

Add $6$ and $2$ .

$3^{8}$

Step 4

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

$6561$