To simplify the expression $2^3 \cdot 2^4$, you can use the product of powers rule, which states:

$a^m \cdot a^n = a^{m+n}$

In this case, both terms have the same base, 2, so you can add the exponents:

$2^3 \cdot 2^4 = 2^{3+4} = 2^7$

Now, calculate $2^7$:

$2^7 = 128$

So, the simplified value is $128$.

Would you like any further details or clarification?

Here are five related questions:

1. How do you simplify expressions with different bases, like $3^2 \cdot 4^2$?
2. What is the product of $2^5 \cdot 2^2$?
3. Can the rule for exponents apply to division, like $2^7 / 2^3$?
4. How do you calculate powers of 10, such as $10^4 \cdot 10^2$?
5. What is the difference between simplifying exponents with the same base and exponents with different bases?

Tip: When multiplying terms with the same base, always add the exponents together!