To determine which of the given expressions is equivalent to [tex]\(-49 x^5\)[/tex], we need to examine and compare them individually:
Given the expressions:
1. [tex]\(-49 x^5\)[/tex]
2. [tex]\(-49 x^6\)[/tex]
3. [tex]\(49 x^6\)[/tex]
4. [tex]\(49 x^5\)[/tex]
Let's compare each one with [tex]\(-49 x^5\)[/tex]:
1. [tex]\(-49 x^5\)[/tex]:
- This expression is exactly the same as our reference expression. Therefore, [tex]\(-49 x^5\)[/tex] is equivalent to itself.
2. [tex]\(-49 x^6\)[/tex]:
- This expression involves the term [tex]\(x^6\)[/tex] instead of [tex]\(x^5\)[/tex].
- Moreover, the coefficient remains [tex]\(-49\)[/tex], but since the power of [tex]\(x\)[/tex] is different, [tex]\(-49 x^6\)[/tex] is not equivalent to [tex]\(-49 x^5\)[/tex].
3. [tex]\(49 x^6\)[/tex]:
- Here, the coefficient is [tex]\(49\)[/tex] (positive) instead of [tex]\(-49\)[/tex] (negative).
- Additionally, the term involves [tex]\(x^6\)[/tex] rather than [tex]\(x^5\)[/tex].
- Both the coefficient and the power of [tex]\(x\)[/tex] are different. Therefore, [tex]\(49 x^6\)[/tex] is not equivalent to [tex]\(-49 x^5\)[/tex].
4. [tex]\(49 x^5\)[/tex]:
- The coefficient here is [tex]\(49\)[/tex] (positive) instead of [tex]\(-49\)[/tex] (negative).
- While the term [tex]\(x^5\)[/tex] is the same, the change in sign means that [tex]\(49 x^5\)[/tex] is not equivalent to [tex]\(-49 x^5\)[/tex].
Therefore, the expression that is equivalent to [tex]\(-49 x^5\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
