Question

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

Answer 1

$9^{\frac{1}{2}}$

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

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

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

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

$2\cdot \frac{1}{2}=1$

$=3^1$

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

$=3$

b)

$27^{\frac{2}{3}}$

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

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

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

$=3^{3\cdot \frac{2}{3}}$

$3\cdot \frac{2}{3} = 2$

$3^2=9$

Hope I helped you!

Success!

Answer 2

A) 1/3 / 0.3 (recurring
b) 9