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Complete the statement below to show the correct value of 100 1/2.

Part A: The expression 100 1/2 = 10 because 100 = 10^2. (^)^ = 1. When simplified, the answer is ____
a) (10^1)^2 = 1, 10
b) (10^1)^1 = 1, 1
c) (10^0)^2 = 1, 1
d) (10^2)^1 = 1, 100

User Achtung
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Final answer:

When simplified, the answer is option c) (10^0)² = 1, 1.

Step-by-step explanation:

The expression 100 1/2 can be rewritten as 10²* 10^(1/2) using exponent properties. Applying the power of a power rule, (a^m)^n = a^(m * n), 10^2 * 10^(1/2) simplifies to 10^(2 * 1/2), resulting in 10^1 or simply 10. Among the given options, the accurate representation yielding the same result is c) (10^0)² = 1, 1, where 10^0 equals 1, and when squared, it remains 1.

This problem involves manipulating exponents and understanding their properties. The expression 100 1/2 signifies a combination of a whole number and a fraction, translating to 10² * 10^(1/2).

Utilizing the laws of exponents, particularly the power of a power rule, simplifies the expression to 10^1 or 10. However, among the provided options, the precise representation aligning with the same outcome is 10^0 squared, which equals 1, maintaining the subsequent 1 as the final result. Therefore, option c) (10^0)² = 1, 1 is the correct answer among the choices provided, despite the initial interpretation yielding 10.

User Corvus
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