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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 convert the number (10000)₇ from base 7 to decimal (base 10) representation.
Step 3:: Break Down the Base 7 Number
From right to left, the place values are $$7^{0}, 7^{1}, 7^{2}, 7^{3}, 7^{4}$$.
In base 7, each digit represents a power of 7.
Step 4:: Expand the Number
10000_{7} = 1 \times 7^{4} + 0 \times 7^{3} + 0 \times 7^{2} + 0 \times 7^{1} + 0 \times 7^{0}
Step 5:: Calculate Each Term
- $$0 \times 7^{0} = 0
- 0 \times 7^{3} = 0
Step 6:: Sum the Terms
2401 + 0 + 0 + 0 + 0 = 2401
Final Answer
10000_{7} = 2401_{10}
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