Sort these in order:
4*3^2, 2*4^3, -4*3^2, 4*-3^2, 4*3^-2
Doing this from low to high is:
-4*3^2, 4*-3^2, 4*3^-2, 4*3^2, 2*4^3
The thing that bothers me is 4*-3^2. I would of stupidly made it 36 and not -36. (i.e. 4*-3^2 = 4*9 = 36.. But instead its 4*(-3^2) = -4*3^2 = -4*9 = -36
I might of skipped something awhile back or forgotten it. Is the general rule in these cases to remove the parentheses and add the negative to beginning? Or do we say that -x^2 would always be negative (which doesn't make sense to me) I'm a little confused here, sorry!
If I wanted to be sure it was positive I think I would say:
4 * (-3)^2
Yeah I get that one, it's written 4*-3^2 though in this case. I just don't understand why the 4 takes on the negative instead.
Don't worry, I'm here to help you understand the correct way to solve expressions like -4*3^2.
When it comes to evaluating mathematical expressions, it is important to understand the order of operations, also known as PEMDAS. This acronym stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
According to the order of operations, exponents (powers) are evaluated before multiplication. So, in the expression -4*3^2, you need to calculate 3^2 first, which is 9. Therefore, the expression simplifies to -4*9, and the final answer is -36.
To clarify your confusion, the general rule is not to always remove the parentheses and add the negative to the beginning. Instead, the negative sign applies to the entire expression within the parentheses. In this case, -4*3^2 means that the square of 3 is obtained first, then multiplied by -4. Alternatively, you can think of it as -4*(3^2) to emphasize that the entire expression inside the parentheses is being negated.
Remember, when you encounter an expression involving negatives, parentheses can help clarify the intended calculations. Applying the order of operations correctly ensures that you get the correct result.
I hope this explanation clears up your confusion. If you have any more questions, feel free to ask!