Question 1202471
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What binomial power does the binomial expansion 1/x^4 + 8/x + 24x^2 + 32x^5 + 16x^8 represent? 
Indicate the binomial base as well as the exponent. Explain how you figured out your answer.
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We have 5 terms ordered according increasing degrees of x.


First term  {{{1/x^4}}}  is the fourth degree of {{{1/x}}}.

The last, 5-th term, is the fourth degree of  {{{2x^2}}}.

Therefore, it is logical to hypothesize that the given expression 
is the binomial expansion of  {{{(1/x + 2x^2)^4}}}.


To check this hypothesis, we should make direct FOIL.


If you do it, you will see that all the terms are correct.


<U>ANSWER</U>.  {{{1/x^4}}} + {{{8/x}}} + {{{24x^2}}} + {{{32x^5}}} + {{{16x^8}}} = {{{(1/x+2x^2)^4}}}.
</pre>

Solved, with explanations.