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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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Math Expert
Joined: 02 Sep 2009
Posts: 46284
If a^2=5, the expression (3^(a+b)^2)/(3^b^2)*9^(-ab) is equal to which [#permalink]

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24 Sep 2015, 22:36
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:14) correct 17% (03:05) wrong based on 148 sessions

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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

Kudos for a correct solution.

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Current Student
Joined: 05 Apr 2015
Posts: 423
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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25 Sep 2015, 05:04
2
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.

Regards,
Dom.
Intern
Joined: 06 Sep 2014
Posts: 11
Location: India
Concentration: General Management, Strategy
GMAT 1: 710 Q47 V40
GPA: 3.8
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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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25 Sep 2015, 08:43
1
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
Intern
Joined: 04 Jun 2008
Posts: 6
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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27 Sep 2015, 00:31
1
[3^(a^2+2ab+b^2) / 3^(b^2)] * 1 / (3^2ab)

Simplify to:
3^(a^2) => 3^5 = 243
Manager
Joined: 29 Jul 2015
Posts: 159
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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27 Sep 2015, 10:00
1
2
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.

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

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

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

= $$3^{a^2}$$

=$$3^5$$

=$$243$$

Director
Joined: 04 Dec 2015
Posts: 700
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
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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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.
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Joined: 09 Sep 2013
Posts: 7027
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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29 May 2018, 21:52
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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] 29 May 2018, 21:52
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