1. The problem is to simplify the expression $A=2^{\frac{3}{-4^{17}}}$. 2. First, recognize the exponent: $\frac{3}{-4^{17}}$. This means $3$ divided by $-4$ raised to the 17th power. 3. Calculate $-4^{17}$. Since the exponent applies only to 4, and the negative sign is outside, $-4^{17} = -(4^{17})$. 4. So the exponent is $\frac{3}{-(4^{17})} = -\frac{3}{4^{17}}$. 5. Rewrite $A$ as $2^{-\frac{3}{4^{17}}}$. 6. Using the property of exponents, $a^{-b} = \frac{1}{a^b}$, we get $A = \frac{1}{2^{\frac{3}{4^{17}}}}$. 7. This is the simplified form of $A$. Since $4^{17}$ is a very large number, the exponent $\frac{3}{4^{17}}$ is very small, so $A$ is close to 1 but slightly less than 1. Final answer: $$A = 2^{-\frac{3}{4^{17}}} = \frac{1}{2^{\frac{3}{4^{17}}}}$$