Question

question
which expression is equivalent to ((2^3)^{-2})?
answer
(\bigcirc) (\frac{1}{64}) (\bigcirc) (2) (\bigcirc) (\frac{1}{32}) (\bigcirc) (64)
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Explanation:

Step1: Apply exponent rule \((a^m)^n = a^{m\times n}\)

For \((2^3)^{-2}\), we multiply the exponents: \(3\times(-2)= -6\), so it becomes \(2^{-6}\).

Step2: Apply negative exponent rule \(a^{-n}=\frac{1}{a^n}\)

\(2^{-6}=\frac{1}{2^6}\), and \(2^6 = 64\), so \(\frac{1}{2^6}=\frac{1}{64}\).

Answer:

\(\frac{1}{64}\) (corresponding to the option \(\frac{1}{64}\))