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Step 1:I'll solve this problem step by step using the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to calculate $$100^{6}$$, which means multiplying 100 by itself 6 times.
Step 3:: Expand the Calculation
100^{6} = 100 \times 100 \times 100 \times 100 \times 100 \times 100
Step 4:: Simplify
We can break this down by recognizing that $$100 = 10^{2}
100^{6} = (10^{2})^{6}
Step 5:: Apply Exponent Rule
Using the power rule $$\left(x^{a}\right)^{b} = x^{ab}$$, we get:
100^{6} = 10^{2 \times 6} = 10^{12}
Step 6:: Calculate the Final Value
10^{12} = 1,000,000,000,000
Final Answer
100^{6} = 1,000,000,000,000 (one trillion)
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