How do you multiply #\root[ 3] { 6x ^ { 7} } * \root [ 3] { 4x ^ { 5} }#?

Question

486 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-29T20:53:57

#2x^4·root(3)(3)#

Since both quantities have the same root, we can combine them under one radical:

#= root(3)(6x^7 xx 4x^5)#

#= root(3)(24x^12)#

Note that #24 = 2^3 xx 3#, so we can put a #2# outside the radical:

#= 2root(3)(3x^12)#

We can also put an #x^4# outside the radical, from the laws of exponents (#(x^12)^(1"/"3) = x^(12"/"3) = x^4#):

#= color(red)(ul(2x^4root(3)(3)#