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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu
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Bunuel
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu [#permalink] New post  03 Jun 2018, 10:17
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If a and b are nonzero integers and \(a^{3b} = a^{b-6}\), what is the value of \(b^{a}\)?


(1) \(a^3 = 8\)

(2) \(a^2 = 4\)
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Re: If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu [#permalink] New post  03 Jun 2018, 10:22
1
Kudos
3b = b - 6
So, b = -2
We got value of b.
Now from
Statement 1.
We can get value of a = 2
So b ^a can be known - Sufficient

Statement 2.
Value of a =+2 or -2
Hence Not sufficient.

Option A is answer.
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu [#permalink] New post  04 Jun 2018, 01:51
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Solution



Given:
    • Integers a and b are non-zero
    • Also, \(a^3b = a^{b-6}\)

To find:
    • The value of \(b^a\)

Approach and Working:
    • From the given expression \(a^3b = a^{b-6}\), as a is non-zero, we can write
      o 3b = b – 6
      Or, 2b = -6
      Or, b = -3

Hence, if we can find out the value of a, we can compute the value of \(b^a\)

Analysing Statement 1
    • As per the information given is statement 1, \(a^3 = 8\)
      o From this, we can write, a = 2

Hence, statement 1 is sufficient to answer

Analysing Statement 2
    • As per the information given is statement 2, \(a^2 = 4\)
      o From this, we can write a = 2 or a = -2
    • From this statement, we cannot find out the specific value of a


Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

Answer: A


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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu [#permalink] New post  05 Jun 2018, 05:13
Bunuel wrote:
If a and b are nonzero integers and \(a^{3b} = a^{b-6}\), what is the value of \(b^{a}\)?


(1) \(a^3 = 8\)

(2) \(a^2 = 4\)


we are asked to fin out the value of \(b^a\)

Note:
1. a and b are integers
2. a and b are nonzero.

we are given:

\(a^{3b}\)=\(a^{b-6}\)

3b=b-6
b=-3

statement 1: \(a^3\)=8
\(a^3\)=\(2^3\)
a=2

ultimate we have the value of both a and b
thus statement 1 is sufficient.

statement 2:\(a^2\)=4
a=+2 or -2

2 different values will give us 2 different answers.
thus statement 2 is not sufficient.

A is the best answer.
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