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Write in exponential notation: $\newline$ $(3a^{2}b)^{4}$

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Power property of logarithms

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Q. Write in exponential notation:

\newline

(3a^{2}b)^{4}

Apply Power of Product Property: Apply the power of a product property to the expression. $\newline$ The power of a product property states that $(xy)^n = x^n \times y^n$ . In this case, we have a product of $3$ , $a^2$ , and $b$ , all raised to the power of $4$ . $\newline$ $(3a^{2}b)^{4} = 3^4 \times (a^2)^4 \times b^4$
Simplify Each Part: Simplify each part of the product separately. $\newline$ First, calculate $3^4$ , which is $3 \times 3 \times 3 \times 3$ . $\newline$ $3^4 = 81$ $\newline$ Next, apply the power of a power property to $(a^2)^4$ , which states that $(x^m)^n = x^{m*n}$ . $\newline$ $(a^2)^4 = a^{2*4} = a^8$ $\newline$ Lastly, $b^4$ remains as it is since it's already in exponential form.
Combine Simplified Parts: Combine the simplified parts to write the final expression in exponential notation. $\newline$ The final expression is the product of $81$ , $a^8$ , and $b^4$ . $\newline$ $81 \times a^8 \times b^4$

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