Question
(S) \( 2^{3} \cdot 2^{-5} \cdot 3^{-3} \cdot 3^{2} \)
Ask by Hall Carroll. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \(\frac{1}{12}\) or \(0.0833\).
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Beyond the Answer
To simplify \( 2^{3} \cdot 2^{-5} \cdot 3^{-3} \cdot 3^{2} \), you can use the laws of exponents. Start by combining the powers of the same base. For the base \( 2 \): \[ 2^{3} \cdot 2^{-5} = 2^{3 + (-5)} = 2^{-2} \] And for the base \( 3 \): \[ 3^{-3} \cdot 3^{2} = 3^{-3 + 2} = 3^{-1} \] Now, putting it all together: \[ 2^{-2} \cdot 3^{-1} = \frac{1}{2^{2}} \cdot \frac{1}{3^{1}} = \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12} \] Therefore, the simplified expression is: \[ \frac{1}{12} \]
