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

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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#