Question

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(3 b^{4}\right)^{2}$$

Short answer

The simplified expression is \(9b^{8}\).

Step-by-step solution

Identify the Inner Operation

Start by identifying the inner operation in the given expression. Here, \(3b^{4}\) is considered as a single entity because it's within the parentheses.

Apply the Power of a Power Rule

The power of a power rule states that \((a^{m})^{n}=a^{m \times n}\). Use this rule to rewrite the expression. In this case, \(3b^{4}\) is raised to the power 2.

Distribute the Power

Apply the power to both components (3 and \(b^{4}\)) inside the brackets. This is because the distributive law of exponentiation over multiplication states that \((ab)^{n}=a^{n}b^{n}\).Apply this rule so to separately raise both 3 and \(b^{4}\) to the power of 2.

Simplify the Result

Simplify the thus far calculated expression. In this case it means calculating \(3^{2}\) and multiplying the exponents in \(b^{4 \times 2}\).