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Answer:
w^3
Step-by-step explanation:
The multiplicative identity element is 1. That means 1 times anything is just that thing.
1 × w^3 = w^3
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<em>Additional comment</em>
That is one of the reasons why a coefficient of 1 is (almost) never shown.
In algebra, multiplication can be indicated a number of ways.
ab . . . . placing values next to each other (sometimes with a small space)
(a)(b) . . . . placing values next to each other with either or both in parentheses
a·b . . . . . using a multiplication symbol between the values.
There are several different multiplication symbols in common use:
* — asterisk
· or • — centered dot
× — centered "x" multiplication symbol
x — the lower-case letter x (when it cannot be confused with a variable)
. — a period (when it cannot be confused with a decimal point). This is uncommon in the US, but is seen occasionally when some of the other symbols are not available. It is more common outside the US.
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The multiplication of a constant and a variable expression <em>cannot actually be accomplished</em>. It can only be "indicated." If you wanted to multiply 2*w^3, that product would be indicated in any of the ways described above. Perhaps the simplest and least-confusing to most people is ...
2w^3
Multiplying 1*w^3 can be indicated the same way: 1*w^3. In view of the special treatment given to a coefficient of 1, we would not simplify this to
1w^3
Rather, we would simplify it to ...
w^3
