SOLUTION: I have previously asked this question, question #853406, but didn't really get help. Find all real solutions to the equation. t^-3/2=64 The answer that I was given was 1/1

Algebra ->  Equations -> SOLUTION: I have previously asked this question, question #853406, but didn't really get help. Find all real solutions to the equation. t^-3/2=64 The answer that I was given was 1/1      Log On


   

Question 854657: I have previously asked this question, question #853406, but didn't really get help.
Find all real solutions to the equation.
t^-3/2=64
The answer that I was given was 1/16, however, I don't know how they got this answer. Can someone please help in showing or explaining the work on how to get to this conclusion?
Thank you in advance for the help.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe you misunderstood the notation according to what you were given? Try the equation as highlight_green%28t%5E%28-3%2F2%29=64%29 and solve for t accordingly. (If problems in rendering, the exponent is negative three halves).

Here is a few steps into solving. (unfortunately, the rendering is still bad).
1%2F%28t%5E%283%2F2%29%29=64 because of the given negative exponent;
t%5E%283%2F2%29=1%2F64=1%2F%282%5E3%2A2%5E3%29
t%5E%283%2F2%29=1%2F%282%5E6%29
...Can you see what steps can be done next? Can you finish and have t=1%2F16?

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I have previously asked this question, question #853406, but didn't really get help.
Find all real solutions to the equation.
t^-3/2=64
The answer that I was given was 1/16, however, I don't know how they got this answer. Can someone please help in showing or explaining the work on how to get to this conclusion?
Thank you in advance for the help.


t%5E%28-3%2F2%29+=+64

t%5E%28%28-+3%2F2%29%2A%282%2F3%29%29+=+64%5E%282%2F3%29 



t%5E-1+=+64%5E%282%2F3%29

t%5E-1+=+4%5E2

t%5E-1+=+16

1%2Ft%5E1+=+16

1%2Ft+=+16

16t = 1 ------ Cross-multiplying

highlight_green%28t+=+1%2F16%29



You can do the check!! 



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