Simplify the Radical Expression ((a^12)/(b^6))^(1/6)

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

Apply the product rule to $\frac{a^{12}}{b^{6}}$ .

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

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

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

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

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

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

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

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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