SOLUTION: Simplify answer and check by raising it back to the 4th power. Please show work. {{{ sqrt( 81x^4y^16z^28 ) }}}

Algebra ->  Radicals -> SOLUTION: Simplify answer and check by raising it back to the 4th power. Please show work. {{{ sqrt( 81x^4y^16z^28 ) }}}      Log On


   



Question 1006922: Simplify answer and check by raising it back to the 4th power. Please show work.

+sqrt%28+81x%5E4y%5E16z%5E28+%29+

Found 2 solutions by fractalier, Edwin McCravy:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
The fourth root of
+sqrt%28+81x%5E4y%5E16z%5E28+%29+ = +/- +3xy%5E4z%5E7
because
%28+3xy%5E4z%5E7%29%5E4 = 81x%5E4y%5E16z%5E28

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
That's a square root not a fourth root.

+sqrt%28+81x%5E4y%5E16z%5E28+%29+

The square root is the 2nd root, so write in the understood index, 2.

+root%282%2C+81x%5E4y%5E16z%5E28+%29+

Write 81 as 92

+root%282%2C+9%5E2x%5E4y%5E16z%5E28+%29+

Divide the index 2 into each exponent and
that removes the square root since 2 will go into
each exponent evenly, without leaving any remainder.

9%5E1x%5E2y%5E8z%5E14

9x%5E2y%5E8z%5E14


Edwin