GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 21:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1044
Location: India
GPA: 3.64
If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

### Show Tags

04 Mar 2018, 10:41
1
1
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:30) correct 6% (01:05) wrong based on 46 sessions

### HideShow timer Statistics

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) $$7^{864}$$

_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going...
Senior SC Moderator
Joined: 22 May 2016
Posts: 3581
If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

### Show Tags

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

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

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

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

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
If a#b = (a^b)^3, the value of (7#6)#8 is  [#permalink]

### Show Tags

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.

_________________
If a#b = (a^b)^3, the value of (7#6)#8 is   [#permalink] 25 Mar 2018, 07:40
Display posts from previous: Sort by