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what is the value of m?
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Updated on: 26 Aug 2021, 10:37
Updated on: 26 Aug 2021, 10:37
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Question Stats:
72% (01:46) correct
27% (00:56) wrong based on 11 sessions
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If \(\frac{(0.00000016 * 10^m) }{ (800 * 10^{-5})} = 0.02 * 10^{14}\), what is the value of m?
A. 15
B. 16
C. 17
D. 18
E.19
A. 15
B. 16
C. 17
D. 18
E.19
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Status:Founder & Quant Trainer
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Re: what is the value of m?
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25 Aug 2021, 04:38
25 Aug 2021, 04:38
2
1
cbrelax wrote:
If \(\frac{(0.00000016 * 10^m) }{ (800 * 10^{-5})} = 0.02 * 10^{14}\), what is the value of m?
A. 15
B. 16
C. 17
D. 18
E.19
A. 15
B. 16
C. 17
D. 18
E.19
\((0.00000016 * 10^m) = 16(10^{-8})(10^m) = 16(10^{m-8})\)
\((800 * 10^{-5}) = 8(10^2)(10^{-5}) = 8(10^{-3})\)
\(0.02 * 10^{14} = 2(10^{-2})(10^{14}) = 2(10^{12})\)
\(\frac{16(10^{m-8})}{8(10^{-3})} = 2(10^{12})\)
\(2(10^{m-8+3}) = 2(10^{12})\)
\((10^{m-5}) = (10^{12})\)
When the bases are equal, the powers are equal
Thus, \(m - 5 = 12\)
\(m =17\)
Hence, option C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: what is the value of m?
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11 Nov 2021, 12:48
11 Nov 2021, 12:48
cbrelax wrote:
If \(\frac{(0.00000016 * 10^m) }{ (800 * 10^{-5})} = 0.02 * 10^{14}\), what is the value of m?
A. 15
B. 16
C. 17
D. 18
E.19
A. 15
B. 16
C. 17
D. 18
E.19
Given: \(\frac{0.00000016 * 10^m }{ 800 * 10^{-5}} = 0.02 * 10^{14}\)
Multiply both sides of the equation by \(800\) to get: \(\frac{0.00000016 * 10^m }{ 10^{-5}} = 16 * 10^{14}\)
Rewrite \(0.00000016\) as \(16 * 10^{-8}\) to get: \(\frac{16 * 10^{-8} * 10^m }{ 10^{-5}} = 16 * 10^{14}\)
Divide both sides by \(16\) to get: \(\frac{10^{-8} * 10^m }{ 10^{-5}} = 10^{14}\)
Multiply both sides by \(10^{-5}\) to get: \(10^{-8} * 10^m = 10^{9}\)
Divide both sides by \(10^{-8}\) to get: \(10^m = 10^{17}\)
Since the bases are equal, we know that the exponents are equal.
So, \(m = 17\)
Answer: C
