Question

Helppp

Express 27^1/2 as a power of 3
Express root 2 as a power of 8
Express root 2/16 as a power of 2

Answer 1

FOR THE FURST QUESTION.

`{27}^{ (1)/(2) } \\ = (3^(3) )^{ (1)/(2) } \\ = {3}^{3 * (1)/(2) } \\ = 3^{ (3)/(2) }`

FOR THE SECOND QUESTION

`√(2) \\ = ( \sqrt[3]{8} )^{ (1)/(2) } \\ = ( {8}^{ (1)/(3) } )^{ (1)/(2) } \\ = 8^{ (1)/(3) * (1)/(2) } ) \\ = 8^{ (1)/(6) }`

FOR THE THIRD ONE

`( √(2) )/(16) \\ = ( √(2) )/(16) \\ = \frac{ {2}^{ (1)/(2) } }{ {2}^(4) } \\ = 2^{ (1)/(2) - 4 } \\ = 2^{ - (7)/(2) }`

ATTACHED IS THE SOLUTION