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