1,261,000 * (0.05(1+0.05)^3) / ((1+0.05)^3-1)

To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The expression is:

\[ 1,261,000 \times \left( \frac{0.05(1+0.05)^3}{(1+0.05)^3 - 1} \right) \]

### Step-by-Step Solution:

1. **Evaluate inside the parentheses:**
   \[
   1 + 0.05 = 1.05
   \]

2. **Raise 1.05 to the power of 3:**
   \[
   1.05^3 = 1.157625
   \]

3. **Calculate the numerator:**
   \[
   0.05 \times 1.157625 = 0.05788125
   \]

4. **Calculate the denominator:**
   \[
   1.157625 - 1 = 0.157625
   \]

5. **Form the fraction:**
   \[
   \frac{0.05788125}{0.157625} = 0.367164
   \]

6. **Multiply by 1,261,000:**
   \[
   1,261,000 \times 0.367164 \approx 462,999.804
   \]

### Final Answer:
\[
462,999.804
\]

Would you like more details on any of the steps? Do you have any questions?

Here are 5 questions you might ask next:
1. How do you simplify expressions with exponents?
2. Can you help me solve a quadratic equation?
3. How do you find the derivative of a function?
4. What are the properties of logarithms?
5. Can you explain the Pythagorean theorem?

**Tip:** When working with fractions in complex expressions, simplify the numerator and denominator separately before dividing.

Learn how to calculate the expression 1,261,000 multiplied by the fraction (0.05 times (1 plus 0.05 cubed)) divided by ((1 plus 0.05 cubed) minus 1). This problem involves arithmetic operations, exponents, and fractions. Suitable for high school students.

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