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.