Question

What expression is equivalent to?? Thanks in advance!!

Answer 1

`( { \frac{ {4}^{ (5)/(4) }. { 4}^{ (1)/(4) } }{ {4}^{ (1)/(2) } } })^{ (1)/(2) } \\ = {( \frac{ {4}^{ (5)/(4) + (1 )/(4) } }{ {4}^{ (1)/(2) } } )}^{ (1)/(2) } \\ = ({ \frac{ {4}^{ (6)/(4) } }{ {4}^{ (1)/(2) } } })^{ (1)/(2) } = \frac{ {4}^{ (6)/(4) * (1)/(2) } }{ {4}^{ (1)/(2) * (1)/(2) } } = \frac{ {4}^{ (3)/(4) } }{ {4}^{ (1)/(4) } } \\ = {4}^{ (3)/(4) - (1)/(4) } = {4}^{ ( 2)/(4) } = {4}^{ (1)/(2) } = √(4) = 2`