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What is the exponent of the last term of: $(2x^2+3y^3)^{10}$

Hi! I'm sorry if this question seems a bit amateurish. I'm quite confused with this question that was asked in a quiz about binomial expansion.

My teacher said that the answer is 30. However, isn't 30 the exponent of y and not the exponent of the whole last term? The b term would be: $3y^3$ and so the last term would be $(3y^3)^{10}=3^{10}y^{30}$

Isn't the answer suppose to be 10 since the exponent of: $3y^3$ is 10.

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    please think how you like. You already have the solution in mind then no need to ask even. Better discuss with your teacher.2012-08-29

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Both the notions "exponent of a term" and "last term" are ill defined. Terms can be ordered arbitrarily, and can be expanded, thereby changing their composition without loosing their identity (i.e., most people would consider it to still be the same term, although it looks different). However if you ask for the exponent in the term $(3y^3)^{10}$ after expansion, then the answer is $30$, since expansion makes that term $59049y^{30}$ which contains only one exponent, $30$. Before expansion it contain two exponents, $3$ and $10$. And strictly speaking a term never has an exponent (attached to it) since a term is by definition an operand of an additive operation, not of exponentiation, so any exponent is part of the term.

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    Good point. I gave it a vote and I marked it as the right answer.2012-08-29
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I think your teacher meant the exponent of the variable $y$, and not of the entire term. The number $3^{10}$ would be called the coefficient of the exponent $y^{30}$.

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    @MicoAbrina - sounds like you should talk to your teacher..2012-08-29