tính nhanh
 (9+1)*(9^2+1)*(9^4+1)*(9^8+1)*(9^16+1)

To solve the expression \((9+1) \times (9^2+1) \times (9^4+1) \times (9^8+1) \times (9^{16}+1)\), let's proceed step by step:

1. **Simplify Each Term**:
   - \(9 + 1 = 10\)
   - \(9^2 + 1 = 81 + 1 = 82\)
   - \(9^4 + 1 = 6561 + 1 = 6562\)
   - \(9^8 + 1 = 43046721 + 1 = 43046722\)
   - \(9^{16} + 1 = 1853020188851841 + 1 = 1853020188851842\)

2. **Multiply the Results**:
   Now we multiply all these simplified terms:
   \[
   10 \times 82 \times 6562 \times 43046722 \times 1853020188851842
   \]

3. **Calculate the Result**:
   Let's calculate the product step by step:

   - \(10 \times 82 = 820\)
   - \(820 \times 6562 = 5380840\)
   - \(5380840 \times 43046722 \approx 2.315 \times 10^{14}\)
   - \(2.315 \times 10^{14} \times 1853020188851842 \approx 4.29 \times 10^{29}\)

Thus, the final result is approximately \(4.29 \times 10^{29}\).

### Would you like to see the detailed steps or have any questions?

Here are 5 related questions you might find interesting:
1. What is the significance of powers of 9 in such expressions?
2. How does the distributive property apply in simplifying such expressions?
3. What are the applications of large number approximations in real-world problems?
4. Can you generalize this expression for any base other than 9?
5. What mathematical techniques can be used to simplify the multiplication of very large numbers?

**Tip:** When dealing with large exponents, look for patterns or simplifications before performing calculations.

Learn how to solve the expression (9+1)*(9^2+1)*(9^4+1)*(9^8+1)*(9^16+1) step-by-step with detailed calculations and explanations. Explore the arithmetic of large numbers and exponents in mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation