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Answer
\( 3^{-4} \cdot 3^{-2} = \frac{1}{729} \)
Solution
Calculate or simplify the expression \( 3^{-4} \cdot 3^{-2} \).
Calculate the value by following steps:
- step0: Calculate:
\(3^{-4}\times 3^{-2}\)
- step1: Multiply:
\(3^{-4-2}\)
- step2: Subtract the numbers:
\(3^{-6}\)
- step3: Express with a positive exponent:
\(\frac{1}{3^{6}}\)
- step4: Evaluate the power:
\(\frac{1}{729}\)
The result of \(3^{-4} \cdot 3^{-2}\) is \(\frac{1}{729}\).
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Simplify this solution Bonus Knowledge
Let’s break it down! When multiplying powers with the same base, you simply add the exponents. So, \( 3^{-4} \cdot 3^{-2} = 3^{-4 + (-2)} = 3^{-6} \). And there you have it, you’ve transformed it into a much simpler expression! Now, if we want to express \( 3^{-6} \) in a more friendly way, we can recall that a negative exponent means we take the reciprocal. So, \( 3^{-6} = \frac{1}{3^6} = \frac{1}{729} \). Quite a nifty little trick, eh?
