Question

How do i solve this

Answer 1

`5.\\5^(1)/(4)\cdot5^(1)/(4)\cdot5^(1)/(4)=5^{(1)/(4)+(1)/(4)+(1)/(4)}=5^(3)/(4)=\sqrt[4]{5^3}=\sqrt[4]{125}\\\\/\text{used:}\ a^n\cdot a^m=a^(n+m)/\\6.\\\left(5^(1)/(4)\right)^6=5^{(1)/(4)\cdot6}=5^{(1)/(2)\cdot3}=5^(3)/(2)=5^{1(1)/(2)}=5\sqrt5\\\\/\text{used:}\ (a^n)^m=a^(n\cdot m)/`

`7.\\5^{-(1)/(4)}=(1)/(5^(1)/(4))=(1)/(\sqrt[4]5)\\\\/\text{used:}\ a^(-n)=(1)/(a^n)/\\8.\\5^2\cdot5^(1)/(4)=5^{2+(1)/(4)}=5^{2(1)/(4)}=5^(9)/(4)=5^2\sqrt[4]5=25\sqrt[4]5`


`a^(m)/(n)=\sqrt[n]{a^m}`