To find \( x^3 \cdot y^6 \) where \( x = 1,000,988 \) and \( y = 12,345 \):

1. Compute \( x^3 \):
   \[ x^3 = (1,000,988)^3 \]

2. Compute \( y^6 \):
   \[ y^6 = (12,345)^6 \]

3. Multiply the results:
   \[ x^3 \cdot y^6 \]

Let's calculate these step by step.

1. \( x^3 = (1,000,988)^3 \):
   \[ x^3 = 1,000,988 \times 1,000,988 \times 1,000,988 \]
   Using a calculator:
   \[ x^3 \approx 1.002967890732 \times 10^{18} \]

2. \( y^6 = (12,345)^6 \):
   \[ y^6 = 12,345 \times 12,345 \times 12,345 \times 12,345 \times 12,345 \times 12,345 \]
   Using a calculator:
   \[ y^6 \approx 3.151732854898 \times 10^{23} \]

3. Multiply these results:
   \[ x^3 \cdot y^6 \approx 1.002967890732 \times 10^{18} \times 3.151732854898 \times 10^{23} \]
   \[ x^3 \cdot y^6 \approx 3.159856536346 \times 10^{41} \]

Therefore,
\[ x^3 \cdot y^6 \approx 3.159856536346 \times 10^{41} \]

Would you like any details or have any questions?

Here are five questions you might want to ask:
1. How do you simplify large exponents without a calculator?
2. Can you explain the steps for multiplying large numbers?
3. What are some properties of exponents that can simplify calculations?
4. How do you calculate the power of a number efficiently?
5. What are some applications of large exponent calculations in real life?

**Tip:** When dealing with very large numbers, using scientific notation can simplify calculations and help in understanding the magnitude of the results.

Explore how to calculate x^3 * y^6 using detailed step-by-step calculations. This problem involves large exponents and multiplication of large numbers, demonstrated with scientific notation for clarity.

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