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The problem is asking you to simplify the expression \((8.7x)(7x)\) using the properties of operations.

### Step-by-step solution:
1. First, apply the distributive property (which in this case is just multiplication):
   \[
   (8.7x)(7x) = 8.7 \times 7 \times x \times x
   \]

2. Multiply the constants (numbers) first:
   \[
   8.7 \times 7 = 60.9
   \]

3. Now, multiply the variables \(x \times x = x^2\).

4. Put it all together:
   \[
   (8.7x)(7x) = 60.9x^2
   \]

### Final answer:
\[
(8.7x)(7x) = 60.9x^2
\]

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

Here are 5 related questions to further explore:
1. What is the distributive property and how does it apply to multiplication of variables?
2. How do you simplify expressions with variables and exponents?
3. What happens when you multiply more complex polynomials?
4. How do you handle division of similar expressions with variables?
5. What are some real-world applications of multiplying algebraic expressions?

**Tip:** Always group constants and variables separately when simplifying expressions.

Learn how to simplify the algebraic expression (8.7x)(7x) using multiplication and properties of exponents. This problem teaches key algebraic techniques, like the distributive property and exponent rules. Suitable for Grade 7 students.

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