Is (xy)^3 the same as xy^3? Explain why or why not.
Nope. The x is cubed also.
I still do not understand how they are different could you please explain it to me?
(xy)^3
Because the xy is in parentheses, the product of x times y is cubed.
xy^3
This expression means that only the y is cubed.
Thank you I understand now. So(xy)3 would be the total of x and y would be cubed. As in xy3 only the y would be cubed then multiplied by x. Do I have it now?
Yes. :-)
Thanks =0)
No, (xy)^3 is not the same as xy^3. This is because the placement of the parentheses changes the order of operations in this expression.
To understand why they are different, let's break down the two expressions:
1. (xy)^3: This expression means to raise the product of x and y to the power of 3. In other words, you multiply x and y together first, and then raise the result to the power of 3.
2. xy^3: This expression means to raise y to the power of 3, and then multiply it by x. Here, you raise y to the power of 3 first, and then multiply the result by x.
To illustrate this with an example, let's say x = 2 and y = 3:
For (xy)^3:
Step 1: xy = 2 * 3 = 6
Step 2: (xy)^3 = 6^3 = 216
For xy^3:
Step 1: y^3 = 3^3 = 27
Step 2: xy^3 = 2 * 27 = 54
As you can see, the two expressions yield different results. Therefore, it is important to pay attention to the placement of parentheses when dealing with exponents in an expression.