It's the set of priority rules for applying operations.

Parentheses or brackets first; then exponents (powers); then divide and multiply; and lastly addition and subtraction.

Thus, for example, 6 + 3 x 4 means 6 + (3 x 4) and not (6 + 3 ) x 4. ie. Do the multiply before the addition. All scientific calculators use these rules. (The early calculators could only do calculations as they were input.)

So the expression -a^2 requires that the power is evaluated (a^2) before the minus is applied; thus - a^2 = -(a^2)

So, is a = 5, the correct evaluation is - (5^2) = -25

If you want to force the subtract first then brackets should be used: (-a)^2 means -a times -a = +a^2

Reference: https://www.mathsisfun.com/operation-order-bodmas.html

Bob

]]>-a^2 is not equal to -1×a^2

PROOF

if a=5 -a^2=(-5)^2=-5×-5=+25 but -1×a^2=-1×5^2=-1×25=-25

So -25 is not equal to +25

Know that -a^2 means -1 x a^2 and not -a x -a.

The reason is that -a^2 has its coefficient as -1

Therefore -a x -a = a^2 and and not -a^2.

This symbol ^ implies exponent.

True but (-a)^2 is totally different.

We know that (-a)^2 = (-a)(-a) = a^2.

How about -(a)^2?

Let me see.

-[(a)(a)]

-(a^2)

-a^2

Agree?

]]>The reason is that -a^2 has its coefficient as -1

Therefore -a x -a = a^2 and and not -a^2.

This symbol ^ implies exponent.]]>