SOLUTION: 1. t^2/3= 4 - ("t" to the power of 2/3 equals 4). Please show me how to work it and not just give an answer. Thanks

Algebra ->  Square-cubic-other-roots -> SOLUTION: 1. t^2/3= 4 - ("t" to the power of 2/3 equals 4). Please show me how to work it and not just give an answer. Thanks       Log On


   

Question 244598: 1. t^2/3= 4 - ("t" to the power of 2/3 equals 4). Please show me how to work it and not just give an answer. Thanks

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Exponent rules:
%28x%5Ea%29%5Eb = x%5E%28ab%29
.
So, for your problem:
t%5E%282%2F3%29=+4
I could raise both to the reciprocal power (3/2) to both sides:
%28t%5E%282%2F3%29%29%5E%283%2F2%29=+4%5E%283%2F2%29
t%5E%282%2F3+%2A3%2F2%29=+4%5E%283%2F2%29
t%5E1=+4%5E%283%2F2%29
t+=+4%5E%283%2F2%29
We can rewrite the right side as:
t+=+%284%5E3%29%5E%281%2F2%29
But, raising something to the 1/2 is essentially taking the square root:
t+=+sqrt%284%5E3%29
t+=+sqrt%284%2A4%2A4%29
We can take "pairs" out from under the radical:
t+=+4sqrt%284%29
t+=+4%2A2
t+=+8