Question

Does -a ? = (-a)?? Explain why or why not.

Answer 1

I think this is referring to exponents? No these are not equivalent. Because in the order of operations, exponents are evaluated before multiplication and a minus sign is like multiplying by -1. But if you remember, parentheses are evaluated before exponents are. So if you have -a ^2, you would get a negative answer, because you square a before multiplying by -1. But if you have (-a)^2, you end up with a positive number, because -1^2 is 1. If the exponent is odd, though, then you would get the same answer regardless, because (for example) -1 ^3 is -1. Hope this makes sense, let me know if I can clarify further!

Answer 2

Step-by-step explanation:

Always remember that variables have coefficients (x is the same as 1·x or 1x).

Raising a base to either an odd or even exponent has particular rules when it comes to signs:

• If you raise -a² = -a² because a has a coefficient of - 1. This implies that -a² = -1a².
• Now, raising -a³ (odd exponent) still results in -a³ because you're only raising the base, a, to its exponent, and it doesn't include its coefficient of -1. Hence, -a³ = -1a³ = -a³.

• Also, (-a²) = -a² because once again, you're only raising the base, a, and not its coefficient (even if both are inside the parenthesis).

It will be different if the base is raised as follows:

• (-a)² = a² because the coefficient, -1, is included within the parenthesis. It is the same as (-1a)² = 1a² or a².
• (-a)³ = -a³ or -1a³ because it is an odd exponent, and if you raise a negative base to an odd exponent results in a negative value of the base.

The key is that the exponent outside the parenthesis will affect both the coefficient and its base, such as (-a)².

Hope this makes complete sense.