Simplify (a^(3m-6))^(2/3)

${(a^{3 m - 6})}^{\frac{2}{3}}$

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

$a^{(3 m - 6) \frac{2}{3}}$

Apply the distributive property.

$a^{3 m \frac{2}{3} - 6 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 m$ .

$a^{3 (m) \frac{2}{3} - 6 (\frac{2}{3})}$

Cancel the common factor.

$a^{3 m \frac{2}{3} - 6 (\frac{2}{3})}$

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$a^{m \cdot 2 + 3 (- 2) \frac{2}{3}}$

Cancel the common factor.

$a^{m \cdot 2 + 3 \cdot - 2 \frac{2}{3}}$

Rewrite the expression.

$a^{m \cdot 2 - 2 \cdot 2}$

Multiply $- 2$ by $2$ .

$a^{m \cdot 2 - 4}$

Move $2$ to the left of $m$ .

$a^{2 m - 4}$