Simplifying (6*10^2)^3
This expression involves both exponents and parentheses. To simplify it, we need to follow the order of operations (PEMDAS/BODMAS):

Parentheses first: Calculate the value inside the parentheses.
 6*10^2 = 6 * 100 = 600

Exponent: Now we have (600)^3. This means we multiply 600 by itself three times.
 600^3 = 600 * 600 * 600 = 216,000,000
Therefore, (6*10^2)^3 simplifies to 216,000,000
Understanding the Steps:
 Exponents: The notation 10^2 represents 10 multiplied by itself twice (10 * 10). The exponent indicates the number of times the base number is multiplied by itself.
 Order of Operations: The order of operations is crucial for solving mathematical expressions correctly. Parentheses are evaluated first, followed by exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
This problem demonstrates how understanding the order of operations and exponent rules can help us simplify complex expressions.