How do you multiply #\root[ 5] { 2} \cdot \root [ 3] { 5} \cdot \root [ 6] { 4}#?

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Answer 1 · 2017-06-15T03:28:18

#2^(8/15) xx 5^(1/3)#

First, rewrite the problem using exponents:

#2^(1/5) xx 5^(1/3) xx 4^(1/6)#

#4# is simply #2^2#:

#2^(1/5) xx 5^(1/3) xx 2^(2/6)#

Now we have two numbers with base #2#. We are allowed to add those exponents together:

#2^(1/5+2/6) xx 5^(1/3)#

Let's focus on the exponent for #2# for now:

#1/5+2/6#

Simplify #2/6#

#1/5+1/3#

Now use common denominators. Multiply #1/5# by #3/3# and #1/3# by #5/5#:

#1/5(3/3)+1/3(5/5)#

This becomes:

#3/15+5/15#

Add the numerators together:

#8/15#

So our solution is:

#2^(8/15) xx 5^(1/3)#