### Instruction: Find $4^4 \cdot 5^4$.### Response: I notice that $4^4 \cdot 5^4$ can be written as $(4 \cdot 5)^4$, using the property that $(a \cdot b)^n = a^n \cdot b^n$.
This makes the calculation much easier, because I only have to raise one number to the fourth power, instead of two.
I know that $4 \cdot 5 = 20$, so I need to find $20^4$.
I can use the fact that $20 = 2 \cdot 10$, and apply the same property again to get $20^4 = (2 \cdot 10)^4 = 2^4 \cdot 10^4$.
I recall that $2^4 = 16$ and $10^4 = 10,000$, so I can multiply them to get $20^4 = 16 \cdot 10,000 = 160,000$.