Problem

The expression $\left(3 x^{4}\right)^{2}$ can be written in the form $3^{a} x^{b}$ where:
- $a=$
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- $b=$
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Answer

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Answer

Final Answer: \(b=\boxed{8}\)

Steps

Step 1 :The given expression is \(\left(3 x^{4}\right)^{2}\).

Step 2 :We can simplify this expression by applying the power of a power rule in exponents, which states that \((a^{m})^{n} = a^{mn}\). Here, \(a\) is \(3x^{4}\) and \(n\) is \(2\).

Step 3 :So, we can rewrite the expression as \(3^{2} x^{4*2}\).

Step 4 :Final Answer: \(a=\boxed{2}\)

Step 5 :Final Answer: \(b=\boxed{8}\)

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