Question

Write your answer as a power or as a product of powers. $$ (3 b)^{3} \cdot b $$

Short answer

The expression simplifies to \(27b^4\).

Step-by-step solution

Break Down the Expression

First, break down \((3b)^3\) into \(3^3 * b^3\), resulting in \(27b^3\). The given problem becomes \(27b^3 * b\).

Apply the Multiplication Rule

In the second step, apply the multiplication rule for expressions with the same base; when the base is the same (in this case, \(b\)), we add the exponents. So, \(b^3 * b\) can be rewritten as \(b^{3+1}\), which equals to \(b^4\). The expression now looks like \(27*b^4\).

Final Simplification

The final step simply involves writing the final answer. Here, \(27*b^4\) remains the same as the expression is already simplified.