Simplify (2^(-3))^2.

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Multiple Choice

Simplify (2^(-3))^2.

Explanation:
Power of a power and negative exponents are the key ideas here. When you raise a power to another power, you multiply the exponents: (a^m)^n = a^{mn}. A negative exponent means a reciprocal: a^{-k} = 1/a^k. So (2^(-3))^2 becomes 2^{(-3)·2} = 2^(-6) = 1/2^6 = 1/64. Equivalently, 2^(-3) = 1/8, and squaring gives (1/8)^2 = 1/64.

Power of a power and negative exponents are the key ideas here. When you raise a power to another power, you multiply the exponents: (a^m)^n = a^{mn}. A negative exponent means a reciprocal: a^{-k} = 1/a^k.

So (2^(-3))^2 becomes 2^{(-3)·2} = 2^(-6) = 1/2^6 = 1/64. Equivalently, 2^(-3) = 1/8, and squaring gives (1/8)^2 = 1/64.

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