Simplify:

$open curly brackets 5 left parenthesis 8 to the power of 1 third end exponent plus 27 to the power of 1 third end exponent right parenthesis cubed close curly brackets to the power of 1 fourth end exponent space space space space space space$

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Solution

open curly brackets 5 left parenthesis 8 to the power of 1 third end exponent plus 27 to the power of 1 third end exponent right parenthesis cubed close curly brackets to the power of 1 fourth end exponent space space space space space space

equals open square brackets 5 open curly brackets left parenthesis 2 cubed right parenthesis to the power of 1 third end exponent plus left parenthesis 3 cubed right parenthesis close curly brackets close square brackets to the power of 1 fourth end exponent

equals left parenthesis 5 to the power of 1 5 cubed right parenthesis to the power of 1 fourth end exponent equals left parenthesis 5 to the power of 1 plus 3 end exponent right parenthesis to the power of 1 fourth end exponent equals left parenthesis 5 to the power of 4 right parenthesis to the power of 1 fourth end exponent equals 5 to the power of 4 straight x 1 fourth end exponent equals 5 to the power of 1 equals 5

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