SOLUTION: Work out the value of 9 to the power of -3/2 Could you please give a method which doesn't use a calculator.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Work out the value of 9 to the power of -3/2 Could you please give a method which doesn't use a calculator.      Log On


   

Question 599571: Work out the value of 9 to the power of -3/2
Could you please give a method which doesn't use a calculator.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Work out the value of 9 to the power of -3/2
the reciprocal will get rid of the negative; exponent 1/2 is the same as square root, so write it
1%2F9%5E%283%2F2%29 = 1%2F%28sqrt%289%5E3%29%29,
factor inside the radical to reveal a perfect square
1%2F%28sqrt%289%5E2%2A9%29%29,
extract the perfect square
1%2F%289%2Asqrt%289%29%29,
we know what the square root of 9 is
1%2F%289%2A3%29 = 1%2F27