sparky16 2 years ago (y+1)^(2/3)=9

1. sparky16

Solve

2. JamesJ

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

3. sparky16

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

4. JamesJ

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

5. sparky16

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

6. sparky16

???

7. JamesJ

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

where do you get the 1/2?

9. JamesJ

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

10. sparky16

where do we go from there?

11. JamesJ

$9^{3/2} = 9^{3 \times 1/2} = 9^{ 1/2 \times 3} = (9^{1/2})^3 = 3^3 = 27$ 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

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

13. JamesJ

Do you understand this one?

14. sparky16

yes

15. JamesJ

Post your new problem as a new problem