How do you write #root5(32)# as a fractional exponent?

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Answer 1 · 2017-01-23T12:05:07

#32^(1/5)=(2^5)^(1/5)=2^(5xx(1/5))=2^(5/5)=2^1=2#

We can write

#root(5)(32)#

using a fractional exponent this way:

#32^(1/5)#

But we can rewrite #32=2^5#, and so:

#(2^5)^(1/5)#

We can use the rule that #(x^a)^b=x^(ab)# to say that:

#(2^5)^(1/5)=2^(5xx(1/5))=2^(5/5)=2^1=2#

So we can write 2 with an exponential as #2^1#