Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is 0.25.
Solution
Calculate or simplify the expression \( 3^{-2} \cdot 6^{2} \cdot 2^{-4} \).
Calculate the value by following steps:
- step0: Calculate:
\(3^{-2}\times 6^{2}\times 2^{-4}\)
- step1: Multiply the numbers:
\(2^{2}\times 2^{-4}\)
- step2: Multiply:
\(2^{2-4}\)
- step3: Subtract the numbers:
\(2^{-2}\)
- step4: Express with a positive exponent:
\(\frac{1}{2^{2}}\)
- step5: Evaluate the power:
\(\frac{1}{4}\)
The result of \(3^{-2} \cdot 6^{2} \cdot 2^{-4}\) is \(\frac{1}{4}\) or 0.25.
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Simplify this solution Bonus Knowledge
To simplify the expression \( 3^{-2} \cdot 6^{2} \cdot 2^{-4} \), we can rewrite \( 6^{2} \) as \( (2 \cdot 3)^{2} = 2^{2} \cdot 3^{2} \). Now our expression looks like: \[ 3^{-2} \cdot (2^{2} \cdot 3^{2}) \cdot 2^{-4} \] Next, we can combine the like terms: \[ 3^{-2} \cdot 3^{2} = 3^{0} = 1 \] And for the base 2: \[ 2^{2} \cdot 2^{-4} = 2^{2 - 4} = 2^{-2} \] So, the entire expression simplifies to: \[ 2^{-2} \cdot 1 = 2^{-2} \] Finally, we can express \( 2^{-2} \) as: \[ \frac{1}{2^{2}} = \frac{1}{4} \] Thus, the final answer is: \[ \frac{1}{4} \]
