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Why this:
$(3 \ast (3^{k-1} + 1) - 2)$
equals to:
$(3 \ast 3^{k-1} + 3 - 2)$
and why/how from this we get to this:
$(3^k + 1)$

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Just evaluate from left to right, giving precedence to parentheses, exponents, multiplication, division, addition, subtraction (in that order, respectively). See solomoan's answer for more specifics to your particular question. –  Mr_CryptoPrime Apr 12 '11 at 9:06
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1 Answer

up vote 0 down vote accepted

Because $a*(b+c)=a*b+a*c$ and $x^m*x^n=x^{m+n}$

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