The given expression is:

$2^{-3} + \frac{1}{2^3}$

Step 1: Simplify $2^{-3}$

Using the property of exponents: $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$

Step 2: Simplify $\frac{1}{2^3}$

This is already in its simplest form: $\frac{1}{2^3} = \frac{1}{8}$

Step 3: Add the two terms

Now, we add the two fractions: $\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$

Final Answer:

The simplified result is: $\boxed{\frac{1}{4}}$

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What is the value of $2^{-2} + \frac{1}{2^2}$?
2. How do you simplify $3^{-2} + \frac{1}{3^2}$?
3. What is $5^{-1} + \frac{1}{5^1}$?
4. How can you express $2^{-4} + \frac{1}{2^4}$?
5. What is the result of $4^{-2} + \frac{1}{4^2}$?

Tip: When dealing with negative exponents, always remember that $a^{-n} = \frac{1}{a^n}$.