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Evaluate
a) 9^-1/2
b) 27^2/3


Sagot :

[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]

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