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

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Status: Preparing for GMAT
Joined: 25 Nov 2015
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If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

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04 Mar 2018, 10:41
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Question Stats:

97% (01:31) correct 3% (00:37) wrong based on 43 sessions

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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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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

$$7 = a$$ 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: $$a$$ # $$b$$= $$(a^b)^3$$

$$((7^{18})^8)^3 =$$

$$(7^{(18*8)})^3 =$$

$$(7)^{(18*8*3)} = (7)^{(144*3)}= 7^{432}$$

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

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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.

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