To simplify the given expression [tex]\( 3w - 3w^3 u^8 - 5u^7 \)[/tex], let's break it down and analyze each term:
1. The first term is [tex]\( 3w \)[/tex].
2. The second term is [tex]\( -3w^3u^8 \)[/tex]. This term combines the variable [tex]\( w \)[/tex] raised to the power of 3 with another variable [tex]\( u \)[/tex] raised to the power of 8, and is multiplied by [tex]\(-3\)[/tex].
3. The third term is [tex]\( -5u^7 \)[/tex]. This term consists of the variable [tex]\( u \)[/tex] raised to the power of 7 and is multiplied by [tex]\(-5\)[/tex].
Now, let's combine all these terms together to form the simplified expression:
[tex]\[
3w - 3w^3u^8 - 5u^7
\][/tex]
When we examine each term, we see that they have different variable compositions and powers. Therefore, no further simplification (like factoring or combining like terms) is possible.
Thus, the simplified expression is:
[tex]\[
-3u^8w^3 - 5u^7 + 3w
\][/tex]
This expression is already in its simplest form.
