Why is -3^2=-9?? Shouldn't it be +9?

Question

Can anyone please explain why it is negative?

My understanding is -3^2=-3x-3........which should equal positive 9...

What is the difference between the above and (-3)^2?

I am obviously missing something, please help!!

Thanks so much!!

Please, if you can, try to explain -4^-2 (why is it = to -1/16?) and 4^-2 (why is it equal to 1/16?).

Thanks again!

Answer 1

When you write -x^2 you mean -(x^2)

In the same way -3^2 means -(3^2) = -9

(-3)^2 is 9 and (-x)^2 = x^2

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-4^-2
means
-(4^(-2))
= -(1/(4^2))
= -1/16

Answer 2

-3^2 written without brackets means -(3^2), and not (-3)^2.
The first is equal to -9, and the second to 9.

This is a straightforward application of the principles embodied in the mnemonic PEMDAS, which indicates order of operations in mathematical expressions. Exponentiation precedes subtraction.

Answer 3

(-3)^2 = (-3) x (-3) = 9

-(3)^2 = (-1) x (3)^2 = (-1) x 9 = -9

Answer 4

It's because of order of operations.

-3^2 = -9, BUT

(-3)^2 = 9

Think of the first part in this way:

- (3 * 3), which is the same as (-1)(3 * 3), or (-1)(9), or -9.

Think of the second equation in this way:

(-3)^2 = (-3)*(-3)

Which is, of course, 9.

Answer 5

In the hierarchy of mathematical operations exponentiation comes before negation. So it should be interpreted as:

-(3^2) = -9

Answer 6

No, -3^2 means -(3^2).

Answer 7

-(3²)=-9
(-3)²=+9
when written -3² it is assumed that the ² only applies to the 3, not the -

The difference is between -3*3=-9 & (-3)(-3)=9

Answer 8

BODMAS

indices (coming under other) comes before multiply

the - sign means x-1