Step-by-step explanation:
[tex]i) \: {(729)}^{ \frac{1}{6} } [/tex]
[tex] = {(3 \times 3 \times 3 \times 3 \times 3 \times 3)}^{ \frac{1}{6} } [/tex]
[tex] = \sqrt[6]{(3 \times 3 \times 3 \times 3 \times 3 \times 3)}[/tex]
= 3 (Ans)
[tex]ii) \: {(64)}^{ \frac{2}{3} } [/tex]
[tex] = \sqrt[3]{ {64}^{2} } [/tex]
[tex] = \sqrt[3]{(64 \times 64)} [/tex]
[tex] = \sqrt[3]{ {2}^{12} } [/tex]
[tex] = {(2)}^{ \frac{12}{3} } [/tex]
[tex] = {2}^{4} [/tex]
= 16 (Ans)
[tex]iii) \: {(243)}^{ \frac{6}{5} } [/tex]
[tex] = {( \sqrt[5]{ {243} })}^{6} [/tex]
[tex] = {3}^{6} [/tex]
= 729 (Ans)
