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Write in exponential notation

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

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

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Power property of logarithms

Full solution

Q. Write in exponential notation

\newline

\left(3 a^{2} b\right)^{4}

Apply Power Rule: Apply the power of a power rule to the expression. $\newline$ The power of a power rule states that $(x^m)^n = x^{(m*n)}$ . We will apply this rule to each part of the expression $(3a^{2}b)^{4}$ .
Apply Rule to $3^4$ : Apply the power of a power rule to the term $3^{4}$ . Since $3$ is a constant, we raise it to the power of $4$ : $(3^1)^4 = 3^{1*4} = 3^4$ .
Apply Rule to $a^8$ : Apply the power of a power rule to the term $a^{(2*4)}$ . $\newline$ For the variable $a$ raised to the power of $2$ , we raise it to the power of $4$ : $(a^2)^4 = a^{(2*4)} = a^8$ .
Apply Rule to $b^4$ : Apply the power of a power rule to the term $b^{4}$ . Since there is no exponent given for $b$ , we assume it is $1$ . Therefore, we raise $b$ to the power of $4$ : $(b^1)^4 = b^{1*4} = b^4$ .
Combine Results: Combine the results from steps $2$ , $3$ , and $4$ . $\newline$ We multiply the results of the individual terms together to get the final expression in exponential notation: $3^4 \times a^8 \times b^4$ .

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