How do you simplify #root4 32#?

2 Answers
Mar 8, 2016

#32 = 16 * 2#
#32^(1/4) = 16^(1/4) * 2^(1/4)#
#= 2 * 2^(1/4)#

Mar 8, 2016

Answer:

#root4 32=2^("5/4")=2root4 2#

Explanation:

We should first note that #32=2^5#.

#=root4(2^5)#

To simplify this, use the rule:

#rootb(x^a)=x^(a"/"b)#

Thus, the expression is equal to

#=2^("5/4")#

This is simplified. However, if you wish, there is another way to simplify it:

#=2^(4"/"4+"1/4")#

#=2^(1+"1/4")#

Use the rule:

#x^(a+b)=x^a(x^b)#

So the expression can be split up into:

#=2^1(2^(1/4))#

Which equals

#=2root4 2#

Another way of approaching this problem is to say that #root4 32# equals

#=root4(2^4*2)#

The #2^4# can be brought out of the root:

#=2root4 2#