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# A quick question about squares and brackets watch

1. 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?
2. (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?
(-4)² is -4 x -4, so 16, whereas -4² is - x 4 x 4, so -16
I think that's right
3. (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
4. 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...
5. (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)
6. (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
7. Your book is wrong to say -4² = 16, because -4² = -16 (as above). However, it is true that (-4)² = 16, and that . It's probably easier to write as , so then you get and . When is even, , but when is odd, .
8. (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.

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.)
9. 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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