Can someone please explain the answer to this question step by step.
8^a(1/4)^b=
1. B=1.5a
2. A=2
I do understand that I can express 8 in powers of 2 so that section becomes 2^3a but how do I express 1/4 in power of 2's?
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8^a(1/4)^b=??? Please Help
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Hi Nadia222,
When posting exponents, please use brackets to avoid any ambiguity. I believe the question should look like this...
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 3a - 2b and replace b with 1.5a to get:
3a - 2b = 3a - 2(1.5a)
= 3a - 3a
= 0
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
Cheers,
Brent
When posting exponents, please use brackets to avoid any ambiguity. I believe the question should look like this...
Target question: What is the value of (8^a)(1/4)^b?Nadia222 wrote:
What is the value of (8^a)(1/4)^b?
1) b = 1.5a
2) a = 2
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 3a - 2b and replace b with 1.5a to get:
3a - 2b = 3a - 2(1.5a)
= 3a - 3a
= 0
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
Cheers,
Brent
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An alternate approach is to test cases.Nadia222 wrote:Can someone please explain the answer to this question step by step.
(8^a)(1/4)^b = ?
1. B=1.5a
2. A=2
Statement 1: b = 1.5a
Case 1: a=2, b=3.
In this case, (8^a)(1/4)^b = (8²)(1/4)³ = (64)(1/64) = 1.
Case 2: a=4, b=6
In this case, (8^a)(1/4)^b = (8�)(1/4)� = (8²)(8²)(1/4)³(1/4)³ = (64)(64)(1/64)(1/64) = 1.
The cases above illustrate that, if b=1.5a, then (8^a)(1/4)^b = 1.
SUFFICIENT.
Statement 2: a=2
Case 1 also satisfies statement 2.
In Case 1, (8^a)(1/4)^b = 1.
Case 3: a=2, b=0
In this case, (8²)(1/4)� = (64)(1) = 64.
Since (8^a)(1/4)^b can be different values, INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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