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

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Properties of logarithms: mixed review

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Q. Write in exponential notation:

\newline

(4n^{-3})^{2}

Apply power rule: We need to apply the power of a power rule which states that $(a^m)^n = a^{m*n}$ . Here, we have $(4n^{-3})^2$ , so we will apply this rule to both the coefficient $4$ and the variable $n$ with its exponent $-3$ .
Apply to coefficient $4$ : First, we apply the rule to the coefficient $4$ . Since $4$ is the same as $4^1$ , we have $(4^1)^2 = 4^{1*2} = 4^2$ .
Apply to variable $n$ : Next, we apply the rule to the variable $n$ with its exponent. We have $(n^{(-3)})^2 = n^{(-3*2)} = n^{(-6)}$ .
Combine results: Now, we combine the results from the coefficient and the variable. We have $4^2 \times n^{-6}$ .
Write in exponential notation: Finally, we write the expression in exponential notation as a single term. Since $4^2$ is a constant, we can write the expression as $16n^{-6}$ .

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