Question

How do I simplify question a

Answer 1

`\left((8a^6)/(b^(18))\right)^(2)/(3)\\\\use:\\\\\left((a)/(b)\right)^n=(a^n)/(b^n)\\\\(a\cdot b)^n=a^n\cdot b^n\\\\\left{(a^n\right)^m=a^(n\cdot m)\\\\\left((8a^6)/(b^(18))\right)^(2)/(3)=(\left(8a^6\right)^(2)/(3))/(\left(b^(18)\right)^(2)/(3))=\frac{8^(2)/(3)(a^6)^(2)/(3)}{b^{18\cdot(2)/(3)}}=\frac{8^(2)/(3)a^{6\cdot(2)/(3)}}{b^(6\cdot2)}=(8^(2)/(3)a^(2\cdot2))/(b^(12))=(8^(2)/(3)a^4)/(b^(12))`


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