Question

Which expression is equivalent to

Answer 1

2

Explanation:

`4^{(1)/(2)}=4^{(1*2)/(2*2)}=4^{(2)/(4)}\\\\a^(m)*a^(n)= a^(m+n)\\\\(a^(m))/(a^(n))=a^(m-n)\\\\\\`

`(\frac{4^{(5)/(4)}*4^{(1)/(4)}}{4^{(1)/(2)}})^{(1)/(2)}=(\frac{4^{(5)/(4)}*4^{(1)/(4)}}{4^{(2)/(4)}})^{(1)/(2)}\\\\\\=(4^[{(5)/(4)+(1)/(4)-(2)/(4)}])^{(1)/(2)}\\\\\\=(4^{(5+1-2)/(4)})^{(1)/(2)}\\\\\\=(4^{(4)/(4)})^{(1)/(2)}\\\\=(4^(1))^{(1)/(2)}\\\\=4^{(1)/(2)}\\\\=√(4) \\\\\\=2`