5 Simplify: (i)(2a3 / 6x-2)3 (ii)(8a3b-4 / 12a-2b2)-2

Dear student 1) 2a36x23=a33x23=a333x23=a927x6 2) 8a3b-412a-2b2-2=23a3--2b-4-2-2 Asaman=am-n=23a5b-6-2=23-2a5-2b-6-2=322a-10b12=94a-10b12 Regards

5. Simplify:
(i)(2a³ / 6x^-2)³
(ii)(8a³b^-4 / 12a^-2b²)^-2

Dear student

1) {(\frac{2 a^{3}}{6 x^{2}})}^{3} = {(\frac{a^{3}}{3 x^{2}})}^{3} = \frac{{(a^{3})}^{3}}{{(3 x^{2})}^{3}} = \frac{a^{9}}{27 x^{6}} 2) {(\frac{8 a^{3} b^{- 4}}{12 a^{- 2} b^{2}})}^{- 2} = {(\frac{2}{3} a^{3 - (- 2)} b^{- 4 - 2})}^{- 2} [A s \frac{a^{m}}{a^{n}} = a^{m - n}] = {(\frac{2}{3} a^{5} b^{- 6})}^{- 2} = {(\frac{2}{3})}^{- 2} {(a^{5})}^{- 2} {(b^{- 6})}^{- 2} = {(\frac{3}{2})}^{2} a^{- 10} b^{12} = \frac{9}{4} a^{- 10} b^{12}

Regards