Could you show me how to get 11/3 in this question?

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Answer 1 · 2018-02-24T08:40:32

E.

The given format can be written as

#a^-1 b^2 (a^2 b^5)^(1/3)#

#= a^(-1+2/3) b^(2+5/3)#

#= a^(-1/3) b^(11/3)#

#= b^(11/3) / a^(1/3)#

Answer 2 · 2018-02-24T08:40:44

Please see the explanation for the proof.

Given: #a^-1b^2root(3)(a^2b^5)#

We can get the following:

#a^-1b^2root(3)(a^2b^5)#

#=a^-1b^2(a^2b^5)^(1/3)# (#because root(n)(a^b)=a^(b/n)#)

#=a^-1b^2a^(2/3)b^(5/3)# (#because (ab)^n=a^nb^n#)

Now we can combine like-terms to get

#=a^(-1+2/3)b^(2+5/3)# (#because a^na^m=a^(n+m)#)

#=a^(-1/3)b^(11/3)#

#=(b^(11/3))/a^(1/3)# (#becauseba^-n=b/(a^n)#)

Therefore, the answer is #E#.

I hope that was clear enough!