Evaluate (a^3)^3*a^-9

${(a^{3})}^{3} \cdot a^{- 9}$

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

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

$a^{3 \cdot 3} \cdot a^{- 9}$

Multiply $3$ by $3$ .

$a^{9} \cdot a^{- 9}$

Multiply $a^{9}$ by $a^{- 9}$ by adding the exponents.

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

$a^{9 - 9}$

Subtract $9$ from $9$ .

$a^{0}$

Simplify $a^{0}$ .

$1$