Question

[81^1/2(64^1/3+125^1/3)]^1/4
Please give answer

Answer 1

$[(81)^{\frac{1}{2}}(64^{\frac{1}{3}}+125^{\frac{1}{3}})]^{\frac{1}{4}}$

$[(9)^{2\times\frac{1}{2}}( \: (4)^{3\times \frac{1}{3}}+(5)^{3\times \frac{1}{3}}\:)]^{\frac{1}{4}}$

$[(9)^{\vancel{2}\times\frac{1}{\cancel{2}}}( \: (4)^{\cancel{3}\times \frac{1}{\cancel{3}}}+(5)^{\cancel{3}\times \frac{1}{\cancel{3}}}\:)]^{\frac{1}{4}}$

$[9(4+5)]^{\frac{1}{4}$

$[9\times9]^{\frac{1}{4}}$

$[3\times3\times3\times3]^{\frac{1}{4}}$

$[(3)^{4}]^{\frac{1}{4}}$

$(3)^{\cancel{4}\times\frac{1}{\cancel{4}}}$

= 3