The expression you provided is:

$(2^{-3})^0 \times 2^{-2}$

Step 1: Simplify $(2^{-3})^0$

By the zero exponent rule, any number raised to the power of 0 is 1:

$(2^{-3})^0 = 1$

Step 2: Multiply by $2^{-2}$

Now, multiply this by $2^{-2}$:

$1 \times 2^{-2} = 2^{-2}$

Step 3: Evaluate $2^{-2}$

To simplify $2^{-2}$, we use the negative exponent rule: $a^{-n} = \frac{1}{a^n}$:

$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

Final Answer:

The value of the given expression is:

$\boxed{\frac{1}{4}}$

Would you like any further explanation or details?

Here are some related questions you might find interesting:

1. What is the general rule for exponents with negative bases?
2. How do you simplify expressions with both positive and negative exponents?
3. What is the zero exponent rule and how is it applied?
4. Can negative exponents apply to fractions and how?
5. What is the difference between powers of zero and powers of one?

Tip: Negative exponents indicate division, not negative values—always think of it as the reciprocal.