Simplify 3^2(3^3)^23^-8

$3^{2} \cdot {(3^{3})}^{2} \cdot 3^{- 8}$

Step 1

Multiply $3^{2}$ by $3^{- 8}$ by adding the exponents.

Move $3^{- 8}$ .

$3^{- 8} \cdot 3^{2} \cdot {(3^{3})}^{2}$

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

$3^{- 8 + 2} \cdot {(3^{3})}^{2}$

Add $- 8$ and $2$ .

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

Step 2

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

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

Step 3

Simplify the expression.

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

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

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

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

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

Multiply $3$ by $2$ .

$\frac{1}{729} \cdot 3^{6}$

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

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

Step 4

Cancel the common factor of $729$ .

Cancel the common factor.

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

Rewrite the expression.

$1$

Simplify 3^2*(3^3)^2*3^-8