How do you rewrite root5 (z^4)5√z4 with rational exponents?

3 Answers
sankarankalyanam
Jun 27, 2018

=> (z^(4/5)) = (root 5 z)^4⇒(z45)=(5√z)4

Explanation:

![http://slideplayer.com/slide/4752256/](useruploads.socratic.org)

root 5 (z^4)5√z4

=> (z^(4/5)) = (root 5 z)^4⇒(z45)=(5√z)4

Jim G.
Jun 27, 2018

z^(4/5)z45

Explanation:

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

•color(white)(x)a^(m/n)=root(n)((a)^m)∙xamn=n√(a)m

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

root(5)(z^4)=z^(4/5)toz>=05√z4=z45→z≥0

Jim S
Jun 27, 2018

Check below

Explanation:

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) AAzinRR

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