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[tex]9^{\frac{1}{2}}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:9=3^2[/tex]
[tex]=\left(3^2\right)^{\frac{1}{2}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0[/tex]
[tex]\left(3^2\right)^{\frac{1}{2}}=3^{2\cdot \frac{1}{2}}[/tex]
[tex]2\cdot \frac{1}{2}=1[/tex]
[tex]=3^1[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a[/tex]
[tex]=3[/tex]
b)
[tex]27^{\frac{2}{3}}[/tex]
[tex]\mathrm{Factor\:the\:number:\:}\:27=3^3[/tex]
[tex]=\left(3^3\right)^{\frac{2}{3}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0[/tex]
[tex]=3^{3\cdot \frac{2}{3}}[/tex]
[tex]3\cdot \frac{2}{3} = 2[/tex]
[tex]3^2=9[/tex]