Simplify
-4^3 – 2 * 4^2
45 ÷ 3^2 – (3-|2-16|)
There should be a line between the top numbers and the bottom, like in a fraction but longer. I typed it on word but when I tried to copy the line never showed when I pasted. Thanks!!
the first question I have is the top:
is it - 4^2 or (-4)^3? turn out, here it will not make a difference. Lucky you.
Lets do the bottom first.
45/9 -(3+14) check that.
45/9-17=
-12
Now the numerator:
-64-2(16)
-64-32
-96
final answer
-96/-12=8
check this
To simplify the expressions, we'll solve each one step-by-step.
1. -4^3 – 2 * 4^2:
-4^3 means raising -4 to the power of 3. According to the Order of Operations (PEMDAS/BODMAS), we should start with the parentheses and then exponentiation. The negative sign is applied after exponentiation, so we won't consider it yet.
-4^3 = -(4^3) = -(4 * 4 * 4) = -64
Now, let's evaluate the second term:
2 * 4^2 = 2 * (4 * 4) = 2 * 16 = 32
Since we have a subtraction operation between the terms, we can simplify the expression further:
-4^3 – 2 * 4^2 = -64 - 32 = -96
Therefore, the simplified result for the first expression is -96.
2. 45 ÷ 3^2 – (3-|2-16|):
Again, we'll follow the order of operations, which means evaluating the parentheses first.
Inside the parentheses, we have |2-16|. The vertical bars (| |) indicate absolute value, which means we discard the negative sign if there is one and only consider the magnitude.
|2-16| = |-14| = 14
Now, let's proceed with the subtraction inside the parentheses:
3 - 14 = -11
Now that we have the value inside the parentheses, we can continue with the exponentiation:
3^2 = 3 * 3 = 9
Now, we can perform the division operation:
45 ÷ 3^2 = 45 ÷ 9 = 5
Finally, we subtract the value inside the parentheses:
5 - (-11) = 5 + 11 = 16
Therefore, the simplified result for the second expression is 16.
I apologize for the inability to include a longer line between the top and bottom numbers. However, I hope this explanation clarifies the simplification process for each expression.