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I posses two Math books, both of which define a certain property of the algebraic manipulation of exponents in different ways.

For example:

Book one would claim that:

2^((3)2+3) = 2(3*5) = 2^15, since 2+3 = 5, and 3*5 = 15.

Book two would claim that:

2^((3)2+3) = 2^(6+3) = 2^9, as (3)2+3 = 9 due to the laws of Bodmas.

I asked my teacher about this, and she said that the method used by book one is correct, however, am very hesitant, as I still do not understand why the laws of Bodmas would not be abided by when algebraically manipulating exponents.

Thanks for any help in advance :)

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    $\begingroup$ Your notation is extremely unclear. Are you asking what $$(x^y)^{a+b}$$ is? $\endgroup$ Commented Mar 23, 2015 at 22:34

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Maybe that none of the two books is wrong. You have to well control the notation that in your question is confused ( learn MathJax basic tutorial and quick reference). Anyway, you can have:

$$ (2^3)^{2+3}=2^{3(2+3)}=2^{15} $$ or: $$ (2^3)^2\cdot 2^3=2^{3\cdot2+3}=2^9 $$

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