How would you simplify #root(4)(32x^4z^19)#?

1 Answer
Jun 25, 2017

#2x\root[4]{2z^{19}}#

Explanation:

#\root[4]{32x^4z^{19}}#

Concepts:
#\root[a]{x^b}=x^{b/a}# or #x^{b\diva}#


Work: Let's split this up.

Part one: #\root[4]{32}=\root[4]{8\cdot4}=\root[4]{(4xx2)\cdot(2xx2)}=\root[4]{((2xx2)xx2)\cdot(2xx2)}#
take out four 2's and you have one 2 remaining: #2\root[4]{2}#
Part two: #\root[4]{x^4}=x^{4\div4}=x^1#, or #x#
Part three: #\root[4]{z^{19}}=z^{19\div4}# which does not get you a whole number exponent, so let's keep it under the #4^{th}# root. #\root[4]{z^{19}}#

Putting it all together: #2\root[4]{2}\cdotx\cdot\root[4]{z^{19}}=2x\root[4]{2z^{19}}#


Source:
Symbolab Step-by-Step