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    Hi,
    Could someone please tell me if (-4)² is the same as -4² and the answer 16 in both cases? Are the brackets superfuous?
    Thanks in advance!
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    (Original post by fasto)
    Hi,
    Could someone please tell me if (-4)² is the same as -4² and the answer 16 in both cases? Are the brackets superfuous?
    Thanks in advance!
    (-4)² is -4 x -4, so 16, whereas -4² is - x 4 x 4, so -16
    I think that's right
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    (Original post by Revolution is my Name)
    (-4)² is -4 x -4, so 16, whereas -4² is - x 4 x 4, so -16
    I think that's right
    This. It is definitely right
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    Thank you!

    This is really confusing me now. I'm not a maths student, I'm just reading up on some stuff because I find it interesting. I bought a big maths textbook that's supposed to cover everything, but it's kind of contradicting what I'm reading online.

    I reasoned the same way you just did, but my book literally explains that if you have a negative base with an even exponent, the result is positive; if you have a negative base with an odd exponent, the result is negative.

    It gives the following examples:
    (I'm writing a to the power of b as a^b because I don't know how to write the 'little' numbers beyond 2)

    -4^2 = 16
    -2^5 = -32

    This contradicts the above. Is it possible that my book is simply wrong!? Is this rule rubbish?

    Edit: My mistake...
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    (Original post by fasto)
    Thank you!

    This is really confusing me now. I'm not a maths student, I'm just reading up on some stuff because I find it interesting. I bought a big maths textbook that's supposed to cover everything, but it's kind of contradicting what I'm reading online.

    I reasoned the same way you just did, but my book literally explains that if you have a negative base with an even exponent, the result is positive; if you have a negative base with an odd exponent, the result is negative.

    It gives the following examples:
    (I'm writing a to the power of b as a^b because I don't know how to write the 'little' numbers beyond 2)

    -4^2 = 16
    -2^5 = -32

    This contradicts the above. Is it possible that my book is simply wrong!? Is this rule rubbish?

    Edit: This site completely contradicts what my book says.
    According to this, "But you could also square -5 to get 25: -5 × -5 = 25"
    I think your book, like a lot of things just assumes the brackets, and takes -4^2 to mean -4 x -4 (16), and -2^5 to mean -2 x -2 x -2 x-2 x -2 (32); so it's not really wrong, it's just not doing something in the correct manner (although a lot of other sources will also make the same assumption)
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    (Original post by Revolution is my Name)
    I think your book, like a lot of things just assumes the brackets, and takes -4^2 to mean -4 x -4 (16), and -2^5 to mean -2 x -2 x -2 x-2 x -2 (32); so it's not really wrong, it's just not doing something in the correct manner (although a lot of other sources will also make the same assumption)
    This.. the book is assuming the brackets.

    Experiment with a calculator...
    (-2)² = 4
    -2² = -(2)² = -(2²)= -4

    if you have a negative base with an even exponent, the result is positive; if you have a negative base with an odd exponent, the result is negative.
    Again, the book is assuming the brackets.
    Even exponent [2]: (-1)² = -1 x -1 = 1 Positive Result
    Odd exponent [3]: (-1)³ = -1 x -1 x -1 = -1 Negative Result
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    Your book is wrong to say -4² = 16, because -4² = -16 (as above). However, it is true that (-4)² = 16, and that (-2)^5 = -32. It's probably easier to write -a as -1 \times a, so then you get -a^n = -1 \times (a^n) and (-a)^n = (-1 \times a)^n = (-1)^n \times a^n. When n is even, (-1)^n = 1, but when n is odd, (-1)^n = -1.
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    (Original post by Revolution is my Name)
    I think your book, like a lot of things just assumes the brackets, and takes -4^2 to mean -4 x -4 (16), and -2^5 to mean -2 x -2 x -2 x-2 x -2 (32); so it's not really wrong, it's just not doing something in the correct manner (although a lot of other sources will also make the same assumption)
    I would be very surprised if any book assumed brackets. The brackets are not optional.

    -4^2=-16
    (-4)^2=16

    What is the title of the textbook?

    I suggest you input your expressions into a scientific calculator and see what happens. (NB Don't use a simple calculator as these don't understand the rules.)
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    I reasoned the same way you just did, but my book literally explains that if you have a negative base with an even exponent, the result is positive; if you have a negative base with an odd exponent, the result is negative.
    Nothing wrong with this, brackets are implicit in the wording: a negative exponent, say -4, squared is (-4)^2.
 
 
 
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