This is the kind of shower thought I have. I am envious of those that have real shower thoughts
(-27)2/3
33 = 27 => 3 = 271/3 => -3 = (-27)1/3 => (-27)2/3 = ((-27)1/3)2 = (-3)2 = 9
Sincere question: why do you put that negative -27 in parentheses?
-27^2/3would come out to a different number, because the exponentiation has a higher precedence than the negationAh, so without parentheses, it would be:
x = -27^2
x / 3?
That doesn’t sound very intuitive though…yup:
(-27)^2/3=((-27) ^ 2) / 3-27^2/3=(-(27 ^ 2)) / 3The reason is that you almost always want the negation to happen after the exponentiation, because it otherwise wouldn’t have any effect (at least when the exponent is even).
Thanks! 😃
Presumably to avoid ambiguity as to whether the thing to exponentiate is 27 or -27.
-272/3 is a different answer and problem than (-27)2/3.
(-27)2 is (-27)(-27) while -272 is (-27)(27).
I like to think of
-27^2as-(27^2).That’s the common shorthand yes, but its still treated like its there.
The other interpretation is just as valid though.
You’re having some complex thoughts.
=(-1)^(2/3) * (3^3)^(2/3) = e^(2*i*pi/3) * 9 = (cos(2pi/3) + i * sin(2pi/3)) * 9 = (-1/2 + i * sqrt(3)/2) * 9
