anonymous
  • anonymous
(y+1)^(2/3)=9
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Solve
JamesJ
  • JamesJ
If (y+1)^(2/3)=9 then (y+1) = 9^(3/2) Now what is 9^(3/2) equal to?
anonymous
  • anonymous
\[\sqrt[2]{9^{3}}\]

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JamesJ
  • JamesJ
Yes, what is the value of that expression. Hint: \( 9^{3/2} = (9^{1/2})^3 = ... \)
anonymous
  • anonymous
I'm not sure... \[729^{1/2}\]
anonymous
  • anonymous
???
JamesJ
  • JamesJ
Yes, but it's easier to write it the way I have because the square root of 9 is 3. Hence \[ 9^{3/2} = (9^{1/2})^3 = 3^3 = 27 \]
anonymous
  • anonymous
where do you get the 1/2?
JamesJ
  • JamesJ
\[ \frac{3}{2} = 3 \times \frac{1}{2} \] hence \[ 9^{3/2} = (9^{1/2})^3 \]
anonymous
  • anonymous
where do we go from there?
JamesJ
  • 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 \( y = ... \)
anonymous
  • anonymous
26! You are a great help! Can u help me with another problem?
JamesJ
  • JamesJ
Do you understand this one?
anonymous
  • anonymous
yes
JamesJ
  • JamesJ
Post your new problem as a new problem

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