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As a math teacher, I would generally not assign such a question - I would employ notation to make the problem more clear. For example -(5^2) vs. (-5)^2.
Mathematical convention??? Not in this Universe where most of us live.
In the world where mathematicians are familiar with the order of operations, I am correct in theory, but incorrect in my explanation which I corrected below.
Quote:
Originally Posted by guidoLaMoto
Your TI-84 is wrong.
No it's not. Try any other calculator with an exponent function and you'll get the same result.
Quote:
Originally Posted by guidoLaMoto
5^2 implies -1 x 5^2 ????.... In other words, every single time you square a positive number you get a negative number?
I forgot to include the - sign when typing that out. So the corrected form is: -5^2 implies -1 x 5^2, or if you prefer, -(5^2), due to the order of operations -- we all remember PEDMAS, right?
In the correct order of operations, exponentiation come before multiplication/division. Five is raised to the second power first, then the product is negated by multiplying it by -1; therefore -5^2 = -25.
If you want to write -5 x -5 as an exponential equation, you would write it (-5)^2 because parenthetical operations come before exponentiation.
In the world where mathematicians are familiar with the order of operations, I am correct in theory, but incorrect in my explanation which I corrected below.
No it's not. Try any other calculator with an exponent function and you'll get the same result.
I forgot to include the - sign when typing that out. So the corrected form is: -5^2 implies -1 x 5^2, or if you prefer, -(5^2), due to the order of operations -- we all remember PEDMAS, right?
In the correct order of operations, exponentiation come before multiplication/division. Five is raised to the second power first, then the product is negated by multiplying it by -1; therefore -5^2 = -25.
If you want to write -5 x -5 as an exponential equation, you would write it (-5)^2 because parenthetical operations come before exponentiation.
The correct answer to the original problem is 50.
It is Sunday, things a little slower, and the end of a week before I go back to work tomorrow. So I'll chime in a little bit.
At least you cite the Order Of Operations.. This is good. My post was..
Quote:
Remember PEMDAS?
PEMDAS
PE MD AS
PE = Parentheses, Exponents
MD = Multiplication, Division
AS = Addition, Subtration
Order Of Operations
Now.. We have the equation (5^2)-(-5^2)
You appear to be implying that you would do the bolded part first, to make it a positive and perhaps MAYBE give you the answer of 50 if you are looking at it that way: (5^2)-(-5^2)
But, I (and most of the people chiming in here) view this as distorting what is actually going on. The first P in PEMDAS is Parentheses.
So, if you are looking inside both Parentheses, look at the second bolded one again: (5^2)-(-5^2)
You have -5 Delta 2, so, -5 multiplied by -5.. The answer here is, of course, +25, or Positive 25, since a negative multiplied by another negative is a positive.
Now, let's look right outside the Parentheses: (5^2)-(-5^2)
That means, that.. The value inside of the Parentheses is being subtracted from the opposite side. That looks like a standard Minus sign to me, not a Negating of the value inside the parentheses.
The first side seems fairly straightforward: 25.
You really do have, in essence, 25 - 25 = 0.
Following.. A - B = C
(5^2)-(-5^2)
A - B
NOW.. YOU BRING UP AN INTERESTING POINT.. THERE WAS NOT A = INCLUDED IN THE ORIGINAL QUESTION, AND IN THIS INSTANCE, YOU COULD LOOK AT IT AS 25 X 25 OR 25-(25) SINCE THAT - IS OUTSIDE OF THE PARENTHESES AND THE ANSWER WOULD BE -625
BUT.. Assuming = is implied.. You get nothing. (Get it? 0? Little math joke)
It is Sunday, things a little slower, and the end of a week before I go back to work tomorrow. So I'll chime in a little bit.
At least you cite the Order Of Operations.. This is good. My post was..
Now.. We have the equation (5^2)-(-5^2)
You appear to be implying that you would do the bolded part first, to make it a positive and perhaps MAYBE give you the answer of 50 if you are looking at it that way: (5^2)-(-5^2)
But, I (and most of the people chiming in here) view this as distorting what is actually going on. The first P in PEMDAS is Parentheses.
So, if you are looking inside both Parentheses, look at the second bolded one again: (5^2)-(-5^2)
You have -5 Delta 2, so, -5 multiplied by -5.. The answer here is, of course, +25, or Positive 25, since a negative multiplied by another negative is a positive.
Now, let's look right outside the Parentheses: (5^2)-(-5^2)
That means, that.. The value inside of the Parentheses is being subtracted from the opposite side. That looks like a standard Minus sign to me, not a Negating of the value inside the parentheses.
The first side seems fairly straightforward: 25.
You really do have, in essence, 25 - 25 = 0.
Following.. A - B = C
(5^2)-(-5^2)
A - B
NOW.. YOU BRING UP AN INTERESTING POINT.. THERE WAS NOT A = INCLUDED IN THE ORIGINAL QUESTION, AND IN THIS INSTANCE, YOU COULD LOOK AT IT AS 25 X 25 OR 25-(25) SINCE THAT - IS OUTSIDE OF THE PARENTHESES AND THE ANSWER WOULD BE -625
BUT.. Assuming = is implied.. You get nothing. (Get it? 0? Little math joke)
(5^2) - (-5^2) = (25) - (-5^2)
(25) - (-5^2) = (25) - (-(5 x 5))
(25) - (-(5 x 5) = (25) - (-25)
(25) - (-25) = 50
The bolded step is where most people get tripped up. According to the order of operations, the exponentiation occurs first, THEN the negation.
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