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24 Feb 2025, 10:02
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:23) correct
0% (00:00) wrong based on 4 sessions
History
Date
Time
Result
Not Attempted Yet
If \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 = 7^x,\) what is the value of \(x\)?
(A) 9
(B) 10
(C) 12
(D) 63
(E) 97
(A) 9
(B) 10
(C) 12
(D) 63
(E) 97
27 Feb 2025, 02:11
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OE
Factor \(7^9\) out of \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9\) to get:
\(7^9 (1 + 1 + 1 + 1 + 1 + 1 + 1) = 7^9 (7)\)
Or, just count that there are seven 7^9’s in the original sum, which can be written as \(7 × 7^9.\) Since \(7^9(7)\) is the same as \(7^9(7^1),\) simplify further: \(7^9(7^1) = 7^{9 + 1} = 7^{10}.\) Thus,
\(x = 10.\)
Note: it is not correct to simply add the original exponents together. When adding or subtracting exponential expressions with the same base, it is not possible to directly combine exponents. Factoring out is the correct procedure.
Answer: B
Factor \(7^9\) out of \(7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9 + 7^9\) to get:
\(7^9 (1 + 1 + 1 + 1 + 1 + 1 + 1) = 7^9 (7)\)
Or, just count that there are seven 7^9’s in the original sum, which can be written as \(7 × 7^9.\) Since \(7^9(7)\) is the same as \(7^9(7^1),\) simplify further: \(7^9(7^1) = 7^{9 + 1} = 7^{10}.\) Thus,
\(x = 10.\)
Note: it is not correct to simply add the original exponents together. When adding or subtracting exponential expressions with the same base, it is not possible to directly combine exponents. Factoring out is the correct procedure.
Answer: B
