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To simplify the given mathematical expression \( 2u^8w^8 \cdot 7u^{-2}w^9 \), we need to combine the terms by using the rules of exponents and multiplication:

1. Multiply the coefficients: \( 2 \cdot 7 = 14 \)
2. Add the exponents for \( u \): \( u^{8 + (-2)} = u^6 \)
3. Add the exponents for \( w \): \( w^{8 + 9} = w^{17} \)

Combining these, the simplified expression is:
\[ 14u^6w^{17} \]

Would you like more details on this or do you have any other questions?

Here are some related questions:
1. How do you simplify expressions with negative exponents?
2. What is the general rule for multiplying variables with exponents?
3. Can you solve for \( u \) if additional conditions are given?
4. How would adding another variable, like \( v \), change the simplification process?
5. What are the implications of having zero as an exponent in an expression?

Tip: When simplifying expressions with multiple variables and exponents, always group and simplify each variable type separately to avoid errors.

Simplify the expression 2u^8w^8 ⋅ 7u^−2w^9 ⋅ 2w^9

Learn how to simplify the expression 2u^8w^8 ⋅ 7u^−2w^9 ⋅ 2w^9 using exponent rules. This problem covers key algebraic concepts such as the multiplication of expressions with variables and the law of exponents. Suitable for students in Grades 8-10.

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