How do you rewrite #root5 (z^4)# with rational exponents?

Question

2202 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-27T09:54:38

#=> (z^(4/5)) = (root 5 z)^4#

#root 5 (z^4)#

#=> (z^(4/5)) = (root 5 z)^4#

Answer 2 · 2018-06-27T10:01:00

#z^(4/5)#

#"using the "color(blue)"law of exponents"#

#•color(white)(x)a^(m/n)=root(n)((a)^m)#

#"here "m=4" and "n=5#

#root(5)(z^4)=z^(4/5)toz>=0#

Answer 3 · 2018-06-27T10:15:38

Check below

#root 5 (z^4)=root 5 (|z|^4)=|z|^(4/5)={(z^(4/5)", "z>=0),((-z)^(4/5)", "z<0):}#

#root 5 (z^4)=|z|^(4/5)# ,#color(white)(a)# #AA##z##in##RR#