Simplify ((a^(1/12)b^-3)^3)^-2

${({(a^{\frac{1}{12}} b^{- 3})}^{3})}^{- 2}$

Multiply the exponents in ${({(a^{\frac{1}{12}} b^{- 3})}^{3})}^{- 2}$ .

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

${(a^{\frac{1}{12}} b^{- 3})}^{3 \cdot - 2}$

Multiply $3$ by $- 2$ .

${(a^{\frac{1}{12}} b^{- 3})}^{- 6}$

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

${(a^{\frac{1}{12}} \frac{1}{b^{3}})}^{- 6}$

Combine $a^{\frac{1}{12}}$ and $\frac{1}{b^{3}}$ .

${(\frac{a^{\frac{1}{12}}}{b^{3}})}^{- 6}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{b^{3}}{a^{\frac{1}{12}}})}^{6}$

Apply the product rule to $\frac{b^{3}}{a^{\frac{1}{12}}}$ .

$\frac{{(b^{3})}^{6}}{{(a^{\frac{1}{12}})}^{6}}$

Multiply the exponents in ${(b^{3})}^{6}$ .

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

$\frac{b^{3 \cdot 6}}{{(a^{\frac{1}{12}})}^{6}}$

Multiply $3$ by $6$ .

$\frac{b^{18}}{{(a^{\frac{1}{12}})}^{6}}$

Multiply the exponents in ${(a^{\frac{1}{12}})}^{6}$ .

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

$\frac{b^{18}}{a^{\frac{1}{12} \cdot 6}}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{b^{18}}{a^{\frac{1}{6 (2)} \cdot 6}}$

Cancel the common factor.

$\frac{b^{18}}{a^{\frac{1}{6 \cdot 2} \cdot 6}}$

Rewrite the expression.

$\frac{b^{18}}{a^{\frac{1}{2}}}$