Which expression leaves you with the smallest number on the number line?
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A.10^8/10^8
B. (10−^2)^−2
C. 10^8/10^10
D. 10^5⋅10^−4
The expression that leaves you with the smallest number on the number line is option B, (10−²)⁻².
To see why, we can simplify each of the expressions:
A. 10⁸/10⁸ = 1
B. (10⁻²)⁻² = (1/10²)⁻² = (1/100)⁻² = 100⁻² = 1/10,000
C. 10⁸/10¹⁰ = 10⁻² = 1/100
D. 10⁵⋅10⁻⁴ = 10¹ = 10
Therefore, the smallest number on the number line is 1/10,000, which corresponds to option B.