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Simplify. Express your answer using a single exponent. $\newline$ $(12c^{9})^{2}$

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Evaluate integers raised to positive rational exponents

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Q. Simplify. Express your answer using a single exponent.

\newline

(12c^{9})^{2}

Apply power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . Here, we have $(12c^{9})^{2}$ , so we apply the rule to both the numerical part and the variable part. $\newline$ $(12c^{9})^{2} = 12^{2} * (c^{9})^{2}$
Calculate numerical power: Calculate the power of the numerical part. $\newline$ We need to square the number $12$ . $\newline$ $12^{2} = 12 \times 12 = 144$
Calculate variable power: Calculate the power of the variable part. $\newline$ Using the power of a power rule for the variable part, we multiply the exponents. $\newline$ $(c^{9})^{2} = c^{9\times2} = c^{18}$
Combine results: Combine the results. $\newline$ Now we combine the results from Step $2$ and Step $3$ to get the final simplified form. $\newline$ $(12c^{9})^{2} = 144c^{18}$

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