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If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which

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Bunuel
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If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   24 Sep 2015, 22:36
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If a^2 = 5, the expression \(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\) is equal to which of the following?

A) 3
B) 9
C) 27
D) 81
E) 243


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E
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kunal555
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   27 Sep 2015, 10:00
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Bunuel wrote:
If a^2 = 5, the expression \(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\) is equal to which of the following?

A) 3
B) 9
C) 27
D) 81
E) 243


Kudos for a correct solution.


\(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\)

= \(\frac{3^{(a^2+b^2+2ab)}}{3^{b^2}}*3^{-2ab}\)

= \(3^{(a^2+b^2+2ab)}*3^{-b^2}*3^{-2ab}\)

= \(3^{a^2}\)

=\(3^5\)

=\(243\)

Answer:-E
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dominicraj
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   25 Sep 2015, 05:04
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9^(-ab) is nothing but 1/(9)^ab.

hence Denominator becomes.. 3^(b)^2 * 3^2(ab)

Further Denominator becomes.. 3^(b^2 + 2ab)

Taking Denominator to numerator.. 3^(a^2+b^2+2ab-b^2-2ab)

= 3^(a)^2.. =243. hence E.

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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   25 Sep 2015, 08:43
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Bunuel wrote:
If a^2 = 5, the expression \(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\) is equal to which of the following?

A) 3
B) 9
C) 27
D) 81
E) 243



Num = 3^(a^2+2ab+b^2) X 3^-2ab
Den = 3^-b^2

Fraction = 3 (a^2 + 2ab + b^2 - 2ab -b^2) = 3 ^ 5 = 243 .... Hence .... E
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   27 Sep 2015, 00:31
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[3^(a^2+2ab+b^2) / 3^(b^2)] * 1 / (3^2ab)

Simplify to:
3^(a^2) => 3^5 = 243
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   23 May 2017, 17:02
Bunuel wrote:
If a^2 = 5, the expression \(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\) is equal to which of the following?

A) 3
B) 9
C) 27
D) 81
E) 243


Kudos for a correct solution.


\(\frac{3^{(a+b)^2}}{3^{b^2}}*9^{-ab}\)
= \(\frac{3^{a^2} * 3^{b^2} * 3^{(2ab)}}{3^{b^2}}\) x \(\frac{1}{3^{(2ab)}}\)
Cancelling out the common terms from numerator and denominator, we get;
\(3^{a^2}\)
\(a^2\) = 5
\(3^5\) = 243.
Answer E...
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink] New post   26 Jan 2021, 12:15
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Re: If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink]
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