Question

simplify.
\\((3b^3a)^4\\)
write your answer without parent

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So, for \((3b^{3}a)^{4}\), we can apply this rule to each factor inside the parentheses.
\((3b^{3}a)^{4}=3^{4}\times(b^{3})^{4}\times a^{4}\)

Step2: Calculate the powers

First, calculate \(3^{4}\). \(3^{4}=3\times3\times3\times3 = 81\).
Next, use the power of a power rule \((x^m)^n=x^{mn}\) for \((b^{3})^{4}\). So, \((b^{3})^{4}=b^{3\times4}=b^{12}\).
And \(a^{4}\) remains as it is.

Step3: Combine the results

Multiply the results together: \(3^{4}\times(b^{3})^{4}\times a^{4}=81\times b^{12}\times a^{4}=81a^{4}b^{12}\)

Answer:

\(81a^{4}b^{12}\)