the equation is 4w^5 times 5w^7. the answer is 9w^12. whats wrong with the answer?

For the expression \(4w^5 \times 5w^7\), the correct way to simplify it involves both multiplying the coefficients (numbers) and adding the exponents of the like terms (the variables). Let's break it down step by step:

1. **Multiply the coefficients** (the numerical parts):  
   \(4 \times 5 = 20\).

2. **Add the exponents** of the variable \(w\):  
   \(w^5 \times w^7 = w^{5+7} = w^{12}\).

Putting it all together:

\[
4w^5 \times 5w^7 = 20w^{12}
\]

The incorrect answer \(9w^{12}\) results from mistakenly adding the coefficients (4 and 5) instead of multiplying them. The correct result should be \(20w^{12}\), not \(9w^{12}\).

Would you like more details or have any questions? Here are some related questions you might find useful:

1. How do you simplify expressions with multiple variables?
2. What is the rule for combining coefficients and exponents?
3. How do you handle division of terms with coefficients and exponents?
4. What are common mistakes when multiplying algebraic expressions?
5. How do you multiply polynomials?

**Tip:** Always multiply the coefficients and add the exponents when dealing with like terms.

Explore the correct method to multiply polynomial expressions with exponents. This example problem involves 4w^5 times 5w^7 and explains why the correct answer is 20w^12, not 9w^12. Suitable for Grades 6-8.

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