Question

Write the value of \[\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} . \]

Answer 1

We have to find the value of. `{5(8^(1/3)+27^(1/3))^3}^(1/4)`So,

 `{5(8^(1/3)+27^(1/3))^3)}^(1/4) ={5(2^(3^xx1/3) +3^(3xx1/3))^3)}^(1/4)`

`= {5(2^(3^xx1/3)+3^(3^xx1/3))^3}^(1/4)`

=`{5(2+3)^3}^(1/4)`

=`{5xx5^3}^(1/4)`

By using rational exponents    `a^mxx a^n = a^(m+n)` we get 

 `{5(8^(1/3)+27^(1/3))^3}^(1/4)` =`{5^(1+3)}^(1/4)`

`=5^(4xx1/4)`

`=5^(4xx1/4)`

`=5^1`

= 5

Hence the simplified value of    `{5(8^(1/3)+27^(1/3))^3}^(1/4)` is 5.