SOLUTION: Please help me solve this problem. The instructions are to simplify this expression. (25a^2b^8)^(1/2) Thank you so much for your help!

Algebra ->  Rational-functions -> SOLUTION: Please help me solve this problem. The instructions are to simplify this expression. (25a^2b^8)^(1/2) Thank you so much for your help!      Log On


   

Question 391270: Please help me solve this problem.
The instructions are to simplify this expression.
(25a^2b^8)^(1/2)
Thank you so much for your help!
Found 2 solutions by mananth, haileytucki:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The instructions are to simplify this expression.
%2825a%5E2b%5E8%29%5E%281%2F2%29
...
%28%285a%29%5E2%2A2%2A%28b%5E4%29%5E2%29%5E%281%2F2%29
..
Take the square root
5a%2Asqrt%282%29%2A%28b%5E4%29
,,,
Sqrt%282%29%2A5a%2Ab%5E4%29
...
m.ananth@hotmail.ca

Answer by haileytucki(390) About Me  (Show Source):
You can put this solution on YOUR website!
(25a^(2)b^(8))^((1)/(2))
Expand the exponent (((1)/(2))) to the expression.
25^((1)/(2))a^(2*((1)/(2)))b^(8*((1)/(2)))
Multiply 2 by each term inside the parentheses.
25^((1)/(2))ab^(8*((1)/(2)))
Multiply 8 by each term inside the parentheses.
25^((1)/(2))ab^(4)
An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent.
((~(25))*ab^(4))
Pull all perfect square roots out from under the radical. In this case, remove the 5 because it is a perfect square.
((5)*ab^(4))
Multiply (5) by ab^(4) to get ab^(4)(5).
(ab^(4)(5))
Multiply ab^(4) by each term inside the parentheses.
5ab^(4)