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

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Director
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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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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) $$7^{864}$$
[Reveal] Spoiler: OA

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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] 04 Mar 2018, 14:33
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# If a#b = (a^b)^3, the value of (7#6)#8 is

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