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

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Power property of logarithms

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Q. Write in exponential notation:

\newline

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

Apply Power Rule: Apply the power of a power rule to the expression $(2a^{2})^{4}$ . $\newline$ The power of a power rule states that $(x^{m})^{n} = x^{m*n}$ . Here, we have a coefficient of $2$ that also needs to be raised to the power of $4$ . $\newline$ $(2a^{2})^{4} = 2^{4} \times (a^{2})^{4}$
Calculate Powers: Calculate the powers separately. $\newline$ First, calculate $2^{4}$ , which is $2 \times 2 \times 2 \times 2 = 16$ . $\newline$ Then, apply the power of a power rule to $a^{2}$ raised to the $4^{\text{th}}$ power, which is $(a^{2})^{4} = a^{2\times4} = a^{8}$ .
Combine Results: Combine the results from Step $2$ . $\newline$ Now, we combine the results of the calculations of $2^{4}$ and $(a^{2})^{4}$ . $\newline$ This gives us $16 \times a^{8}$ .

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