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04 Mar 2018, 10:41
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (01:25) correct
13%
(01:31)
wrong
based on 64
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a#b\) = \((a^b)^3\), the value of \((7#6)#8\) is
A) \(7^{216}\)
B) \(7^{232}\)
C) \(7^{432}\)
D) \(7^{648}\)
E) \(7^{864}\)
A) \(7^{216}\)
B) \(7^{232}\)
C) \(7^{432}\)
D) \(7^{648}\)
E) \(7^{864}\)
04 Mar 2018, 14:33
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souvonik2k
In strange symbol questions with brackets, start with the brackets and apply the rule.
The result of the operation with bracketed numbers becomes the new \(a\).
\(a\) # \(b\) = \((a^b)^3\)
The value of \((7\)#\(6)\)#\(8\) is
1) start with brackets
\(7 = a\) and \(6 = b\)
\(7\) # \(6\)
Rule: \(a\) # \(b\) = \((a^b)^3\)
\((a^b)^3\) =
\((7^6)^3 = (7)^{(6*3)}=7^{18}\)
2) repeat the rule, with a "new" \(a\) and \(b\)
\(7^{18}\) is the new \(a\) as we consider the second part of the expression, which is
\(7^{18}\) # \(8\)
Rule: \(a\) # \(b\)= \((a^b)^3\)
\(((7^{18})^8)^3 =\)
\((7^{(18*8)})^3 =\)
\((7)^{(18*8*3)} = \\
\\
(7)^{(144*3)}= 7^{432}\)
Answer C
25 Mar 2018, 07:40
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Solution
\((7 # 6) # 8 = ({7^6})^3 #8\)
By applying the identity, \(({a^m})^n= a^{(m*n)}\) in \(({7^6})^3\), we can write:
- •\((7 # 6) # 8\) =\((7^{(6*3)}) # 8\)= \((7^{18}) # 8\)
•\((7 # 6) # 8 = ({({7^{18}})^8)}^3\)
•\((7 # 6) # 8 =(7^{(18*8)})^3= 7^{(18*8*3)}\)
•\((7 # 6) # 8 =7^{432}\)
Therefore, the correct answer is C.
Answer: C
