Step-by-step explanation:
[tex] \sf \: We \: have : \bigg( \sqrt[3]{ \sqrt{0.000064} } {\bigg) }^{5} \\ [/tex]
[tex] \sf = \bigg( \sqrt[3]{ \sqrt{ \frac{64}{ {10}^{6} } } } { \bigg)}^{5} \\ [/tex]
[tex] \sf = \bigg( \sqrt[3]{ \sqrt{ \bigg( \frac{8}{ {10}^{3} } } \bigg)^{3} } \bigg)^{5} \\ [/tex]
[tex] \sf = \bigg( \sqrt[3]{ \frac{8}{ {10}^{3} } } \bigg)^{5} \\ [/tex]
[tex] \sf = \bigg( \sqrt[3]{ \frac{ {2}^{3} }{ {10}^{3} } } \bigg)^{5} \\ [/tex]
[tex] \sf = \bigg( \sqrt[3]{ \bigg( \frac{2}{10} \bigg)^{3} } \bigg) ^{5} \\ [/tex]
[tex] \sf = \bigg( \bigg( \frac{2}{10} \bigg) ^{3 \times \frac{1}{3} } \bigg) ^{5} \\ [/tex]
[tex] \sf = \bigg( \bigg( \frac{2}{10} \bigg) ^{ \cancel {\bf{3 }}\times \frac{1}{ \cancel{ \bf3} }} \bigg) ^{5} \\ [/tex]
[tex] \sf = \bigg( \frac{2}{10} \bigg) ^{5 }[/tex]
[tex] \sf = \frac{ {2}^{5} }{ {10}^{5} } \\ [/tex]
[tex] \sf = \frac{2 \times 2 \times 2 \times 2 \times 2}{10 \times 10 \times 10 \times 10 \times 10} \\ [/tex]
[tex] \sf = \frac{32}{100000} \\ [/tex]
[tex] \bf= {\boxed{0.00032}} \\ [/tex]
Another method:
[tex] \sf \: \bigg( \sqrt[3]{ \sqrt{0.000064} } {\bigg) }^{5} \\ [/tex]
[tex] \sf =[ \big{{(0.0000 64) ^{ \frac{1}{2} } \big}} ^{ \frac{1}{3} } { ] }^{5} \\ [/tex]
[tex] \sf = (0.000064) ^{ \frac{1}{2} \times \frac{1}{3} + \times 5} \\ [/tex]
[tex]\sf = (0.000064 {)}^{ \frac{5}{6} } \\ [/tex]
[tex]\sf = \bigg( \frac{64}{1000000} \bigg)^{ \frac{5}{6} } \\ [/tex]
[tex]\sf = \bigg( \frac{ {2}^{6} }{ {10}^{6} } \bigg) ^{ \frac{5}{6} } \\ [/tex]
[tex]\sf = [ \bigg( \frac{2}{10} \bigg) ^{6} ] ^{ \frac{5}{6} }\\ [/tex]
[tex]\sf = \bigg( \frac{2}{10} \bigg) ^{6 \times \frac{5}{6} } \\ [/tex]
[tex]\sf = \bigg( \frac{2}{10} \bigg) ^{ \cancel{ \bf6 }\times \frac{5}{ \cancel{ \bf6}} } \\ [/tex]
[tex]\sf = \bigg( \frac{2}{10} \bigg) ^{5} \\ [/tex]
[tex]\sf = \frac{ {2}^{5} }{ {10}^{5} } \\ [/tex]
[tex]\sf = \frac{2 \times 2 \times 2 \times 2 \times 2}{10 \times 10 \times 10 \times 10 \times 10} \\ [/tex]
[tex]\sf = \frac{32}{100000} \\ [/tex]
[tex] \sf = \boxed{ \sf0.00032}Ans. \\ [/tex]
[tex]\textsf{Please let me know if have any other questions.}\\[/tex]
