## sparky16 Group Title (y+1)^(2/3)=9 one year ago one year ago

1. sparky16 Group Title

Solve

2. JamesJ Group Title

If (y+1)^(2/3)=9 then (y+1) = 9^(3/2) Now what is 9^(3/2) equal to?

3. sparky16 Group Title

$\sqrt[2]{9^{3}}$

4. JamesJ Group Title

Yes, what is the value of that expression. Hint: $$9^{3/2} = (9^{1/2})^3 = ...$$

5. sparky16 Group Title

I'm not sure... $729^{1/2}$

6. sparky16 Group Title

???

7. JamesJ Group Title

Yes, but it's easier to write it the way I have because the square root of 9 is 3. Hence $9^{3/2} = (9^{1/2})^3 = 3^3 = 27$

8. sparky16 Group Title

where do you get the 1/2?

9. JamesJ Group Title

$\frac{3}{2} = 3 \times \frac{1}{2}$ hence $9^{3/2} = (9^{1/2})^3$

10. sparky16 Group Title

where do we go from there?

11. JamesJ Group Title

$9^{3/2} = 9^{3 \times 1/2} = 9^{ 1/2 \times 3} = (9^{1/2})^3 = 3^3 = 27$ Now $$(y+1)^{2/3} = 9$$ is equivalent to $[(y+1)^{2/3}]^{3/2} = 9^{3/2}$ i.e., $(y+1)^1 = 27$ i.e., $y + 1 = 27$ Thus $$y = ...$$

12. sparky16 Group Title

26! You are a great help! Can u help me with another problem?

13. JamesJ Group Title

Do you understand this one?

14. sparky16 Group Title

yes

15. JamesJ Group Title

Post your new problem as a new problem