How do you simplify 9^(1/2) × 3^ (-2/3)?

Answer 1

there are different approaches to the problem; here's two

9^(1/2)*3^(-2/3)

3^(-2/3)=(1/3^[2/3])=(1/[3^2)^(1/3)]=1/9^(1/3)

9^(1/2) * (1/9^(1/3)=9^(1/2)/9^(1/3)=9^(1/2-1/3)=9^(1/6)

9^(1/6)=(3^2)^(1/6)=3^(2/6)=3^(1/3)

9^(1/2)=(3^2)^(1/2)=3

3*3^(-2/3)=3^(1-[2/3])=3^(1/3)