The problem in the image asks for the value of the expression:

$2^3 \cdot 2^2 \cdot 2^1 \cdot 2^0$

Step-by-step solution:

1. Simplify each power of 2:

   • $2^3 = 8$
   • $2^2 = 4$
   • $2^1 = 2$
   • $2^0 = 1$ (anything raised to the power of 0 is 1)

2. Multiply the results: $8 \cdot 4 \cdot 2 \cdot 1 = 64$

So, the value of the expression is 64.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the value of $3^3 \cdot 3^2 \cdot 3^1$?
2. How does the zero exponent rule work for any base?
3. If one term in the product has a negative exponent, how does it change the value?
4. What happens when you multiply terms with different bases but the same exponents?
5. Can the base of an exponent be a fraction? What would that mean?

Tip: Remember, when multiplying powers with the same base, you can add the exponents.