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sparky16
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Solve

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

sparky16
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\[\sqrt[2]{9^{3}}\]

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

sparky16
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I'm not sure... \[729^{1/2}\]

sparky16
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???

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

sparky16
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where do you get the 1/2?

JamesJ
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\[ \frac{3}{2} = 3 \times \frac{1}{2} \] hence
\[ 9^{3/2} = (9^{1/2})^3 \]

sparky16
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where do we go from there?

JamesJ
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\[ 9^{3/2} = 9^{3 \times 1/2} = 9^{ 1/2 \times 3} = (9^{1/2})^3 = 3^3 = 27\]
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 \( y = ... \)

sparky16
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26! You are a great help! Can u help me with another problem?

JamesJ
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Do you understand this one?

sparky16
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yes

JamesJ
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Post your new problem as a new problem