French Salinas
02/24/2024 · Middle School
Simplify. Use positive exponents for any variables. \( \frac{6^{-6} a^{5}}{6^{-3} a^{-4}} \)
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Step-by-step Solution
Calculate or simplify the expression \( (6^{-6} a^{5})/(6^{-3} a^{-4}) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(6^{-6}a^{5}\right)}{\left(6^{-3}a^{-4}\right)}\)
- step1: Remove the parentheses:
\(\frac{6^{-6}a^{5}}{6^{-3}a^{-4}}\)
- step2: Multiply by \(a^{-n}:\)
\(6^{-6}a^{5}\times 6^{3}a^{4}\)
- step3: Multiply the terms:
\(6^{-6+3}a^{5}\times a^{4}\)
- step4: Add the numbers:
\(6^{-3}a^{5}\times a^{4}\)
- step5: Multiply the terms:
\(6^{-3}a^{5+4}\)
- step6: Add the numbers:
\(6^{-3}a^{9}\)
- step7: Evaluate the power:
\(\frac{1}{216}a^{9}\)
The simplified expression using positive exponents is \( \frac{1}{216}a^{9} \).
Quick Answer
\( \frac{1}{216}a^{9} \)
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