the exponent is -2 and not 2.Use the order of operations.
\(\frac{1^{2}}{3} = \frac{1*1}{3} = \frac{1}{3}\)
Makes no difference. A one to any power, positive or negative, is still....one!the exponent is -2 and not 2.
It makes no difference at all-- 1 to the power of anything is still 1.the exponent is -2 and not 2.
Do you not know the order of operations?my last question is about whether the exponent applies to the whole number including the minus which is in front of the number or it applies to the number without the minus if a parenthesis is not used?
Correct.then
-1^2 = -1
(-1)^2 = 1
Am I correct?
Wait a minute!then
-1^2 = -1
(-1)^2 = 1
Am I correct?
But in the first case, according to PEMDAS, it is 1 squared and then the negative sign is applied. The second case removes any ambiguity, by explicitly stating it is negative 1 that is to be squared.Wait a minute!
Both expressions are identical and they are both equal to 1
-1 to any ODD power is -1
-1 to any EVEN power is +1
+1 to any power, ODD or EVEN, is +1
Except there is a difference between how binary subtraction and unary minus actually work and are actually implemented. In particular unary minus can be performed without doing subtraction and requires only a single operand on top of the evaluation stack.As I mentioned before, "-X" is simply a short way of saying "0 - X". According to the order of operations, the negative should be treated as subtraction, and thus -1^2 is the same as -(1^2), or -1.
That is how modern calculators work, for example, because negative is treated as subtraction in the standard order of operations. No ambiguity there.
Perhaps, on the surface they may look different, but I believe the internal workings are the same. There is no "negative" in binary, so instead it uses two's complement and adds the value to zero. This is the same as subtracting from zero. On a software level, subtraction and negatives are handled the same way.Except there is a difference between how binary subtraction and unary minus actually work and are actually implemented. In particular unary minus can be performed without doing subtraction and requires only a single operand on top of the evaluation stack.
In my TI-92 the binary minus followed by a constant actually computes:
ans(1) - const
that is the previous answer minus the constant.
The unary minus is just applied to the constant.
Clearly on this calculator they are different animals.
by Duane Benson
by Aaron Carman
by Aaron Carman