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# What number times (1⁄3)^2 will give the value of 3^3?

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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26 Jan 2016, 05:16
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Question Stats:

89% (00:54) correct 11% (01:19) wrong based on 141 sessions

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What number times (1⁄3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 243

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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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26 Jan 2016, 05:19
1
Let the number be x
x * (1/3)^2 = 3^3
=>x = 3^5
= 243

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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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26 Jan 2016, 11:32
1
Bunuel wrote:
What number times (1⁄3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 243

So, we have (1/3)²(k) = 3³ .............solve for k
We can rewrite (1/3)² as 3ˉ²
So, we get: (3ˉ²)(k) = 3³
Divide both sides by 3ˉ² to get: k = (3³)/ (3ˉ²)
Apply quotient law to get: k = 3⁵ = 243

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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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27 Jan 2016, 22:08
Bunuel wrote:
What number times (1⁄3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 243

My Take:
Indeed it's E) 243

let that number is P
(1/3)^2 X P = 3^2 (given)

P = 3^5 = 243
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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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30 Jan 2016, 11:10
1
Hi All,

The speed with which you can answer many Quant questions on Test Day will come down to how you use the available information you're given AND in how you 'see' the math involved. While this question can certainly be solved using exponent rules, we can do a little math and use the answer choices to our advantage to avoid the rest of that math.

We're asked what number times (1⁄3)^2 will give the value of 3^3.

So... what numbers times 1/9 will get us 27.

(X)(1/9) = 27

If we multiply both sides by 9, we get...

X = (27)(9)

Since (27)(10) = 270, looking at the answer choices, there's really only one answer that makes sense...

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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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08 Feb 2017, 11:24
Bunuel wrote:
What number times (1⁄3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 243

We can create the following equation in which k = the number:

k(1/3)^2 = 3^3

k(1/9) = 27

k = 243

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Re: What number times (1⁄3)^2 will give the value of 3^3?  [#permalink]

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08 Feb 2017, 11:37
Bunuel wrote:
What number times (1⁄3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 243

$$(1⁄3)^2 = 3^{-2}$$

We have : $$3^{-2}*3^k = 3^3$$

So, k = 5

Thus, 3^5 = 243

Answer will hence be (E) 343
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Re: What number times (1⁄3)^2 will give the value of 3^3? &nbs [#permalink] 08 Feb 2017, 11:37
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