https://file.aiquickdraw.com/mathbot/file/17256249226329jvm7hmo.jpg

The image asks to expand two expressions:

1. \( 10^7 \cdot 10^6 \)
2. \( (10^3)^4 \)

Let's expand both:

1. **\( 10^7 \cdot 10^6 \)**:
   By the property of exponents \( a^m \cdot a^n = a^{m+n} \), we can add the exponents:
   \[
   10^7 \cdot 10^6 = 10^{7+6} = 10^{13}
   \]
   So, the expanded form is:
   \[
   10^{13}
   \]

2. **\( (10^3)^4 \)**:
   By the power of a power property \( (a^m)^n = a^{m \cdot n} \), we multiply the exponents:
   \[
   (10^3)^4 = 10^{3 \cdot 4} = 10^{12}
   \]
   So, the expanded form is:
   \[
   10^{12}
   \]

Would you like more detailed explanations on these steps or have any questions? 

Here are 5 related questions:
1. How would you expand \( (2^5)^3 \)?
2. What is the expanded form of \( 5^4 \cdot 5^3 \)?
3. If you have \( (x^2)^5 \), how do you simplify it?
4. Can you combine \( 3^4 \cdot 3^6 \) using exponent rules?
5. How do you simplify \( (4^2)^3 \)?

**Tip**: Always remember that when multiplying exponents with the same base, you add the exponents, and when raising a power to another power, you multiply them.

Write each expression in expanded form: 10^7 * 10^6 and (10^3)^4.

Learn how to expand expressions with exponents such as 10^7 * 10^6 and (10^3)^4. This step-by-step solution covers the key rules of exponents and is suitable for students in Grades 6-8.

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