To simplify the expression $b^4 \cdot b$ and rewrite it in the form $b^n$:

We apply the rule of exponents:

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

Here, we have:

$b^4 \cdot b^1 = b^{4+1} = b^5$

Thus, the simplified form is:

$b^5$

Would you like more details or have any questions?

Here are five related questions to practice:

1. Simplify $b^3 \cdot b^2$.
2. Simplify $x^7 \cdot x^3$.
3. Rewrite $b^6 \cdot b^{-2}$ in the form $b^n$.
4. Simplify $(b^2)^3$.
5. Simplify $b^5 \cdot b^5$.

Tip: When multiplying powers with the same base, simply add their exponents!