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R = 3^{81}
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21 Jan 2021, 03:52
21 Jan 2021, 03:52
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Question Stats:
70% (01:14) correct
30% (02:41) wrong based on 10 sessions
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\(R = 3^{81}\)
\(R^R = 3^S\)
\(S = ?\)
A. \(3\)
B. \(81\)
C. \(3^{81}\)
D. \(3^{85}\)
E. \(3^{87}\)
\(R^R = 3^S\)
\(S = ?\)
A. \(3\)
B. \(81\)
C. \(3^{81}\)
D. \(3^{85}\)
E. \(3^{87}\)
Re: R = 3^{81}
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21 Jan 2021, 04:38
21 Jan 2021, 04:38
1
R^R = (3^81)^(3^81)
= 3^(81*(3^81))
= 3^((3^4)*(3^81))
= 3^(3^(4+81))
= 3^(3^85)
= 3^S
therefore, S= 3^85
correct option is (D)
= 3^(81*(3^81))
= 3^((3^4)*(3^81))
= 3^(3^(4+81))
= 3^(3^85)
= 3^S
therefore, S= 3^85
correct option is (D)
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Re: R = 3^{81}
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21 Jan 2021, 06:38
21 Jan 2021, 06:38
1
Carcass wrote:
\(R = 3^{81}\)
\(R^R = 3^S\)
\(S = ?\)
A. \(3\)
B. \(81\)
C. \(3^{81}\)
D. \(3^{85}\)
E. \(3^{87}\)
\(R^R = 3^S\)
\(S = ?\)
A. \(3\)
B. \(81\)
C. \(3^{81}\)
D. \(3^{85}\)
E. \(3^{87}\)
\(R = 3^{81}\)
So, \(R^R = (3^{81})^{3^{81}}\) [replaced R with 3^81]
\(= (3^{3^4})^{3^{81}}\) [rewrote 81 as 3^4]
\(= 3^{3^{85}}\) [applied power of power rule AND product rule]
So, \(3^{3^{85}} = 3^S\)
So, \(S = 3^{85}\)
Answer: D
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