To rewrite the expression \((4^{-2})^3\) using only positive exponents, we can apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
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Start with the original expression: \[ (4^{-2})^3 \]
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Apply the power of a power property: \[ 4^{-2 \cdot 3} = 4^{-6} \]
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Rewrite the negative exponent using the property \(a^{-n} = \frac{1}{a^n}\): \[ 4^{-6} = \frac{1}{4^6} \]
Thus, the expression \((4^{-2})^3\) rewritten using only positive exponents is: \[ \frac{1}{4^6} \]