To determine which terms are like terms to \(5a^5b^4\), we need to understand what it means for terms to be like terms. Like terms must have the same variables raised to the same power. The coefficients of the terms do not need to be the same.
The given term is \(5a^5b^4\). Here, the variable \(a\) is raised to the 5th power, and the variable \(b\) is raised to the 4th power.
Let's analyze each option:
1. \(a^5b^4\)
- This term has \(a\) raised to the 5th power and \(b\) raised to the 4th power, which matches the given term. Therefore, it is a like term.
2. \(5a^4b^5\)
- This term has \(a\) raised to the 4th power and \(b\) raised to the 5th power, which does not match the given term. Therefore, it is not a like term.
3. \(-2a^5\)
- This term has \(a\) raised to the 5th power but does not have \(b\) raised to the 4th power. Therefore, it is not a like term.
4. \(-a^5b^4\)
- This term has \(a\) raised to the 5th power and \(b\) raised to the 4th power, which matches the given term. Therefore, it is a like term.
5. \(9a^5b^4\)
- This term has \(a\) raised to the 5th power and \(b\) raised to the 4th power, which matches the given term. Therefore, it is a like term.
6. \(2a^5b^5\)
- This term has \(a\) raised to the 5th power, but \(b\) is raised to the 5th power instead of the 4th power. Therefore, it is not a like term.
7. \(6b^4\)
- This term has \(b\) raised to the 4th power, but it does not have \(a\) raised to the 5th power. Therefore, it is not a like term.
Based on this analysis, the terms that are like terms to \(5a^5b^4\) are:
- \(a^5b^4\)
- \(-a^5b^4\)
- \(9a^5b^4\)
So, the selected like terms are: [tex]\(a^5b^4\)[/tex], [tex]\(-a^5b^4\)[/tex], and [tex]\(9a^5b^4\)[/tex].
