(1)
we are given
[tex](36)^{\frac{1}{2} }[/tex]
Firstly, we will find all possible factors of 36
[tex]36=6*6=6^2[/tex]
we can write as
[tex](36)^{\frac{1}{2} }=(6^2)^{\frac{1}{2} }[/tex]
now, we can use property of exponent
[tex](a^m)^n=a^{m*n}[/tex]
we get
[tex](36)^{\frac{1}{2} }=(6)^{2*\frac{1}{2} }[/tex]
[tex](36)^{\frac{1}{2} }=(6)^{1 }[/tex]
[tex](36)^{\frac{1}{2} }=6[/tex]..............Answer
(2)
[tex](27)^{\frac{2}{3} }[/tex]
Firstly, we will find all possible factors of 27
[tex]27=3*3*3=3^3[/tex]
we can write as
[tex](27)^{\frac{2}{3} }=(3^3)^{\frac{2}{3} }[/tex]
now, we can use property of exponent
[tex](a^m)^n=a^{m*n}[/tex]
we get
[tex](27)^{\frac{2}{3} }=(3)^{3*\frac{2}{3} }[/tex]
[tex](27)^{\frac{2}{3} }=(3)^{2 }[/tex]
[tex](27)^{\frac{2}{3} }=3*3[/tex]
[tex](27)^{\frac{2}{3} }=9[/tex]..................Answer
