How do you simplify $root [ 5] { 243x ^ { 25} y ^ { 15} }$ ?

Question

2014 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-14T01:36:44

$3x^5y^3$

$root(5)(243x^25y^15)$

To evaluate a fifth root, convert each part of the radicand (the part of the problem under the radical symbol) to a power of five.

In this example, $243=3^5$ .

And using the exponent rule $(x^a)^b=x^(ab)$ ,
$x^25=(x^5)^5$ and $y^15=(y^3)^5$

$root(5)(3^5 (x^5)^5(y^3)^5)$

The fifth root of a base raised to the fifth power is the base, i.e.
$root(5)(a^5)=a$ .

$root(5)(3^5 (x^5)^5(y^3)^5)=3x^5y^3$

How do you simplify root [ 5] { 243x ^ { 25} y ^ { 15} }root [ 5] { 243x ^ { 25} y ^ { 15} }?