Question

1. simplify the expression.

$(3b^8)^4$
$(3b^8)^4 = \square$
(simplify your an

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((3b^8)^4\), we apply this rule: \(3^4\times(b^8)^4\).

Step2: Simplify each term

First, calculate \(3^4\). \(3^4 = 3\times3\times3\times3 = 81\). Then, use the power of a power rule \((a^m)^n = a^{m\times n}\) for \((b^8)^4\). So, \((b^8)^4 = b^{8\times4}=b^{32}\).

Step3: Combine the results

Multiply the two simplified terms together: \(81\times b^{32}=81b^{32}\).

Answer:

\(81b^{32}\)