Question
Determine the value of the expression \( 4^{3} \cdot 4^{-6} \) A \( 4^{-18} \) B \( \frac{1}{12} \) C -64 D \( \frac{1}{64} \)
Ask by Ball Davies. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of the expression \(4^{3} \cdot 4^{-6}\) is \(\frac{1}{64}\).
Solution
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Bonus Knowledge
To evaluate the expression \( 4^{3} \cdot 4^{-6} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \). So, we have: \[ 4^{3} \cdot 4^{-6} = 4^{3 + (-6)} = 4^{-3} \] Now, \( 4^{-3} \) can be rewritten as: \[ \frac{1}{4^{3}} = \frac{1}{64} \] Thus, the value of the expression is \( \frac{1}{64} \). The correct answer is \( D \) \( \frac{1}{64} \).
