### Instruction: What is $\frac{2^2 \cdot 2^{-3}}{2^3 \cdot 2^{-2}}$?### Response: I want to simplify this fraction by using the rules of exponents.
I can rewrite $2^2 \cdot 2^{-3}$ as $2^{2-3}$ by using the rule that $a^m \cdot a^n = a^{m+n}$.
Similarly, I can rewrite $2^3 \cdot 2^{-2}$ as $2^{3-2}$.
So the fraction becomes $\frac{2^{2-3}}{2^{3-2}}$.
Now I can use another rule of exponents that says $\frac{a^m}{a^n} = a^{m-n}$.
So I can rewrite the fraction as $2^{(2-3)-(3-2)}$.
I can simplify the exponent by doing the arithmetic inside the parentheses.
I get $2^{(2-3)-(3-2)} = 2^{(-1)-(1)} = 2^{-2}$.
Finally, I can use another rule of exponents that says $a^{-n} = \frac{1}{a^n}$.
So I can rewrite $2^{-2}$ as $\frac{1}{2^2}$.
I can evaluate $2^2$ as 4.