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# 8^a*(1/4)^b = ?

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Math Expert
Joined: 02 Sep 2009
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04 Nov 2014, 09:31
1
9
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Difficulty:

45% (medium)

Question Stats:

61% (01:16) correct 39% (01:21) wrong based on 450 sessions

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Tough and Tricky questions: Exponents.

$$8^a*(\frac{1}{4})^b =$$?

(1) b = 1.5a
(2) a = 2

Kudos for a correct solution.

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05 Nov 2014, 00:13
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We have: 8^a*(1/4)^b = 2^3a*2^(-2b) = 2^(3a - 2b)

S1:b = 1.5a --> 2b = 3a --> 3a - 2b = 0
--> 2^0 = 1
SUFF

S2: a = 2
NOT SUFF because we don't know b.

Ans:A
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05 Nov 2014, 00:52
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Bunuel wrote:

Tough and Tricky questions: Exponents.

$$8^a*(\frac{1}{4})^b =$$?

(1) b = 1.5a
(2) a = 2

Kudos for a correct solution.

Question can written as 2^3a*(1/2^2)^b or 2^3a*2-2b...We need to find the value of 2^(3a-2b)

St 1 b=1.5a or 2b=3a so we have 2^0=1..Sufficient

St2 says a=2...but we don't know anything about b...in sufficient

Ans A
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05 Nov 2014, 21:31
1
8^a*(1/4)^b = 2^(3a-2b)

Statement 1 : b = 1.5a => b = 3/2*a => 2b = 3a

Therefore 3a -2b = 0. Hence 2^(3a-2b) = 2^0 =1. Sufficient

Statement 2 : a = 2. It is clearly insufficient
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08 Sep 2017, 21:26
Bunuel wrote:

Tough and Tricky questions: Exponents.

$$8^a*(\frac{1}{4})^b =$$?

(1) b = 1.5a
(2) a = 2

Kudos for a correct solution.

I personally think this is a 700 level question...classic "C" trap anyways

St 1

b =3/2 a

Just plug in a number

8^2 (1/4)^3 = 1 some reciprocal property

St 2

Insuff

A
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18 Jan 2018, 07:52
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Top Contributor
1
Bunuel wrote:

Tough and Tricky questions: Exponents.

$$8^a*(\frac{1}{4})^b =$$?

(1) b = 1.5a
(2) a = 2

Kudos for a correct solution.

Target question: What is the value of (8^a)(1/4)^b?
This is a good candidate for rephrasing the target question.

Let's take (8^a)(1/4)^b and rewrite both parts with the same base of 2.
Notice that 8 = 2^3 and 1/4 = 2^(-2)
So, we can rewrite the original expression as: [(2^3)^ a][2^(-2)]^b
Simplify to get: (2^3a)(2^-2b) [power of a power law]
Combine terms to get: 2^(3a - 2b)
To determine the value of 2^(3a - 2b), we must determine the value of (3a - 2b)
So, let's rephrase the target question.
REPHRASED target question: What is the value of 3a - 2b?

Statement 1: b = 1.5a
Take: b = 1.5a
Multiply both sides by 2 to get: 2b = 3a
Subtract 2b from both sides to get: 3a - 2b = 0
PERFECT!!
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a = 2
Not enough info to determine the value of 3a - 2b
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

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23 Jan 2019, 21:51
Bunuel wrote:

Tough and Tricky questions: Exponents.

$$8^a*(\frac{1}{4})^b =$$?

(1) b = 1.5a
(2) a = 2

Always manipulate the given equation

$$2^{3a}* 2^{-2b} = 2^0$$

3a - 2b = 0
3a=2b
b =1.5 a

Statement 1) True

Statement 2) b can be any value.

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8^a*(1/4)^b = ?   [#permalink] 23 Jan 2019, 21:51
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