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First, we recognize that 81 is a power of the number 3, which means that:
We replace in the problem:
Keep in mind that the numerator and denominator of the fraction have terms with the same base, therefore we use the property of powers to divide between terms with the same base:
We apply it in the problem:
Therefore, the correct answer is option b.
\( (2^3)^6 = \)
Look for patterns! Start with small powers: , , , . Practice recognizing common powers to make these problems faster!
While is correct numerically, the question asks for an exponential form. Since , the answer must be , not just 9.
If you can't express both terms with the same base, then you cannot use the exponent division rule. You'd need to calculate the actual values and divide normally.
The exponent division rule keeps your answer in exponential form, which is often required. Plus, it's much faster than calculating large numbers!
Think: "When dividing, subtract the powers!" means you have 4 threes multiplied, then you're dividing by 2 threes, leaving you with threes.
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