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If a#b = (a^b)^3, the value of (7#6)#8 is

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If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

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New post 04 Mar 2018, 10:41
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A
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C
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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) \(7^{864}\)

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If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

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New post 04 Mar 2018, 14:33
souvonik2k wrote:
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) \(7^{864}\)

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
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If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

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New post 25 Mar 2018, 07:40

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
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