Question 1

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

Question 2

$9^{(1)/(2)}$

$\mathrm{Factor\:the\:number:\:}\:9=3^2$

$=\left(3^2\right)^{(1)/(2)}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc),\:\quad \:a\ge 0$

$\left(3^2\right)^{(1)/(2)}=3^{2\cdot (1)/(2)}$

$2\cdot (1)/(2)=1$

=3^1

$\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a$

b)

$27^{(2)/(3)}$

$\mathrm{Factor\:the\:number:\:}\:27=3^3$

$=\left(3^3\right)^{(2)/(3)}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^(bc),\:\quad \:a\ge 0$

$=3^{3\cdot (2)/(3)}$

$3\cdot (2)/(3) = 2$

3^2=9

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