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