Question

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

Answer 1

$( { \frac{ {4}^{ \frac{5}{4} }. { 4}^{ \frac{1}{4} } }{ {4}^{ \frac{1}{2} } } })^{ \frac{1}{2} } \\ = {( \frac{ {4}^{ \frac{5}{4} + \frac{1 }{4} } }{ {4}^{ \frac{1}{2} } } )}^{ \frac{1}{2} } \\ = ({ \frac{ {4}^{ \frac{6}{4} } }{ {4}^{ \frac{1}{2} } } })^{ \frac{1}{2} } = \frac{ {4}^{ \frac{6}{4} \times \frac{1}{2} } }{ {4}^{ \frac{1}{2} \times \frac{1}{2} } } = \frac{ {4}^{ \frac{3}{4} } }{ {4}^{ \frac{1}{4} } } \\ = {4}^{ \frac{3}{4} - \frac{1}{4} } = {4}^{ \frac{ 2}{4} } = {4}^{ \frac{1}{2} } = \sqrt{4} = 2$