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Answer :
- Identify like terms: $-7x^6$ and $5x^6$.
- Add the coefficients: $-7 + 5 = -2$.
- Combine the new coefficient with the variable term: $-2x^6$.
- The simplified expression is $\boxed{{-2x^6}}$.
### Explanation
1. Identifying Like Terms
We are asked to simplify the expression $-7x^6 + 5x^6$. Notice that both terms contain the same variable $x$ raised to the same power $6$. This means we can combine these terms because they are 'like terms'.
2. Adding Coefficients
To simplify, we add the coefficients of the like terms. The coefficients are the numbers in front of the $x^6$ terms. So we have $-7 + 5$. The result of this addition is $-2$.
3. Writing the Simplified Expression
Now, we write the simplified expression by combining the new coefficient with the variable term $x^6$. This gives us $-2x^6$.
4. Final Answer
Therefore, the simplified expression is $\boxed{{-2x^6}}$.
### Examples
Understanding how to combine like terms is fundamental in algebra and has many practical applications. For example, imagine you are calculating the total cost of materials for a project. If you have 5 pieces of wood that each cost $x^6$ dollars and you need to subtract 7 pieces of the same wood, the expression $-7x^6 + 5x^6$ helps you determine the net cost. Simplifying this expression to $-2x^6$ tells you that you are effectively selling 2 pieces of wood, which impacts your overall budget calculation. This skill is crucial for managing resources and making accurate financial assessments in various real-world scenarios.
- Add the coefficients: $-7 + 5 = -2$.
- Combine the new coefficient with the variable term: $-2x^6$.
- The simplified expression is $\boxed{{-2x^6}}$.
### Explanation
1. Identifying Like Terms
We are asked to simplify the expression $-7x^6 + 5x^6$. Notice that both terms contain the same variable $x$ raised to the same power $6$. This means we can combine these terms because they are 'like terms'.
2. Adding Coefficients
To simplify, we add the coefficients of the like terms. The coefficients are the numbers in front of the $x^6$ terms. So we have $-7 + 5$. The result of this addition is $-2$.
3. Writing the Simplified Expression
Now, we write the simplified expression by combining the new coefficient with the variable term $x^6$. This gives us $-2x^6$.
4. Final Answer
Therefore, the simplified expression is $\boxed{{-2x^6}}$.
### Examples
Understanding how to combine like terms is fundamental in algebra and has many practical applications. For example, imagine you are calculating the total cost of materials for a project. If you have 5 pieces of wood that each cost $x^6$ dollars and you need to subtract 7 pieces of the same wood, the expression $-7x^6 + 5x^6$ helps you determine the net cost. Simplifying this expression to $-2x^6$ tells you that you are effectively selling 2 pieces of wood, which impacts your overall budget calculation. This skill is crucial for managing resources and making accurate financial assessments in various real-world scenarios.
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