8^a*(1/4)^b = ? (1) b = 1.5a (2) a = 2

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

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

No info about B

Insuff

A

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

Answer: A

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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.

Answer A

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

Before we even look at the statements lets rewrite the question prompt: \(2^{3a} * \frac{1^{b}}{2^{2b}}\)

(1) b = 1.5a

\(2^{3a} * \frac{1^{b}}{2^{2b}}\)
= \(2^{2b} * \frac{1}{2^{2b}}\)
= \(\frac{2^{2b}}{2^{2b}}\)
= \(1\)

Sufficient.

(2) a = 2

Don't know what b is; insufficient.

Answer is A.

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