[tex]\left(\dfrac{8a^6}{b^{18}}\right)^\frac{2}{3}\\\\use:\\\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\\left{(a^n\right)^m=a^{n\cdot m}\\\\\left(\dfrac{8a^6}{b^{18}}\right)^\frac{2}{3}=\dfrac{\left(8a^6\right)^\frac{2}{3}}{\left(b^{18}\right)^\frac{2}{3}}=\dfrac{8^\frac{2}{3}(a^6)^\frac{2}{3}}{b^{18\cdot\frac{2}{3}}}=\dfrac{8^\frac{2}{3}a^{6\cdot\frac{2}{3}}}{b^{6\cdot2}}=\dfrac{8^\frac{2}{3}a^{2\cdot2}}{b^{12}}=\dfrac{8^\frac{2}{3}a^4}{b^{12}}[/tex]
[tex]use:\ a^\frac{n}{m}=\sqrt[m]{a^n}\to8^\frac{2}{3}=\sqrt[3]{8^2}=\left(\sqrt[3]{8}\right)^2=2^2=4\\\\answer:\\\\\left(\dfrac{8a^6}{b^{18}}\right)^\frac{2}{3}=\huge\boxed{\frac{4a^4}{b^{12}}}[/tex]
