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Question
write the expression as a single power of 6.\\(\frac{6^{9}}{6^{4}}=\\) ? \\(6^{3}\\)\\(6^{5}\\)\\(6^{13}\\)\\(6^{36}\\)
Step1: Apply exponent quotient rule
When dividing like bases, subtract exponents: $\frac{a^m}{a^n}=a^{m-n}$
So $\frac{6^9}{6^4}=6^{9-4}$
Step2: Calculate exponent difference
$9-4=5$, so $6^{9-4}=6^5$
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$6^5$