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We should must be careful about order of operations when using negative numbers or negative exponents.
-n Before solution of (-1)
Let us see the solution of -1 base to power 2 and 3.
We know that 2 (-1) = 1 And 3 (-1) = -1
therefore -1 to any EVEN power is 1 and -1 to any ODD power is -1. By putting this rule to all integers. We get ...
_ n | (-x) = 1 if n is EVEN | n > (-x) = -1 if n is ODD | _| Similarly -n 1 1 _ (-x) = ------- = ---- if n is EVEN | n x | (-x) | | -n 1 1 > (-x) = ------ = ---- if n is ODD | n -x | (-x) | _|
Final answer will be 1/x when n is EVEN and -1/x when n is ODD.
Here we should must be careful about the negative exponents. First convert into positive exponent and then solve further.
1/3 -2/3 2n - 2n -------------- = ? -2/3 2n
_____________________ / _____________ / / ____ / / / 2 / 4 / 4 . / 4 / \/ \/ / -------------------- / 3 \/ 2