Which is greater 1,000or (6^2)^3? explain

Let's compare \(1,000\) and \((6^2)^3\).

1. First, simplify \((6^2)^3\):
   - \(6^2 = 36\), so the expression becomes \(36^3\).
   - Now, calculate \(36^3\):
     \[
     36^3 = 36 \times 36 \times 36 = 46,656
     \]

2. Now, compare the two numbers:
   - \(1,000\) and \(46,656\).

Clearly, \(46,656\) is much greater than \(1,000\).

Thus, \((6^2)^3\) is greater than \(1,000\).

Would you like more details on any of the steps? Here are some related questions:

1. What is the general method for simplifying exponents like \((a^b)^c\)?
2. How can you calculate large powers like \(36^3\) more quickly?
3. How do exponents affect the growth of numbers?
4. What are the properties of powers and how are they used in simplification?
5. Can you explain how to estimate which number is larger without exact calculations?

**Tip:** When comparing large numbers involving powers, it's helpful to simplify each expression and use properties of exponents to evaluate them more easily.

Which is greater, 1,000 or (6^2)^3? Explain.

Learn how to compare the number 1,000 and (6^2)^3 by simplifying the powers of numbers. This step-by-step guide covers exponentiation rules and shows that (6^2)^3 equals 46,656, which is much greater than 1,000. Suitable for students in Grades 6-8.

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