Multiply -6w^7 and 4w^2. Simplify your answer as much as possible.
Understand the Problem
The question is asking us to multiply two terms, specifically -6w^7 and 4w^2, and then simplify the result as much as possible.
Answer
The simplified answer is \(-24w^{9}\).
Answer for screen readers
The simplified result of the multiplication is (-24w^{9}).
Steps to Solve
- Multiply the coefficients First, multiply the coefficients of the two terms: (-6) and (4).
$$ -6 \cdot 4 = -24 $$
- Add the exponents of the variable Next, add the exponents of (w): (w^{7}) and (w^{2}).
Using the property of exponents (w^m \cdot w^n = w^{m+n}):
$$ w^{7} \cdot w^{2} = w^{7+2} = w^{9} $$
- Combine the results Now, combine the results from steps 1 and 2:
$$ -24w^{9} $$
The simplified result of the multiplication is (-24w^{9}).
More Information
This result shows how to multiply two monomials by handling the coefficients and the variable separately. The final expression combines both parts for a complete answer.
Tips
- Forgetting to apply the exponent rule when adding the exponents of the same base.
- Miscalculating the multiplication of the coefficients, especially when negative numbers are involved.
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