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# 3 ⋅ 3 ⋅ 3 ⋅ 3/9 ⋅ 9 ⋅ 9 ⋅ 9=

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3 ⋅ 3 ⋅ 3 ⋅ 3/9 ⋅ 9 ⋅ 9 ⋅ 9=  [#permalink]

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Updated on: 12 Jul 2018, 23:12
1
1
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:20) correct 11% (00:02) wrong based on 45 sessions

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$$\frac{3 ⋅ 3 ⋅ 3 ⋅ 3}{9 ⋅ 9 ⋅ 9 ⋅ 9}$$=

(A) $$\frac{1}{3}$$^4
(B) $$\frac{1}{3}$$^3
(C) 1/3
(D) 4/9
(E) 4/3

Level: 500

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Originally posted by SajjadAhmad on 14 Oct 2017, 10:44.
Last edited by SajjadAhmad on 12 Jul 2018, 23:12, edited 1 time in total.
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Re: 3 ⋅ 3 ⋅ 3 ⋅ 3/9 ⋅ 9 ⋅ 9 ⋅ 9=  [#permalink]

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14 Oct 2017, 10:53
1
We should understand that (a.a/b.b) can be written as (a/b).(a/b) ----- (1)

Here "." represents multiplication and the above property is valid for multiplication.

Now applying (1) in the problem.

We can write the question as (3/9).(3/9).(3/9).(3/9) which on further simplification gives us (1/3).(1/3).(1/3).(1/3) = (1/3)^4

Hence the answer is A.
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Re: 3 ⋅ 3 ⋅ 3 ⋅ 3/9 ⋅ 9 ⋅ 9 ⋅ 9=  [#permalink]

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14 Oct 2017, 14:01
$$\frac{3 ⋅ 3 ⋅ 3 ⋅ 3}{9 ⋅ 9 ⋅ 9 ⋅ 9}$$=

(A) $$\frac{1}{3}$$^4
(B) $$\frac{1}{3}$$^3
(C) 1/3
(D) 4/9
(E) 4/3

Exponents

$$\frac{3 ⋅ 3 ⋅ 3 ⋅ 3}{9 ⋅ 9 ⋅ 9 ⋅ 9}=$$

$$\frac{3^4}{(3^2)^4}=\frac{3^4}{3^8}= \frac{1}{3^{(8-4)}}= \frac{1}{3^4}=(\frac{1}{3})^4$$

Cancel factors

Factor out four 3s from both numerator and denominator, to yield

$$\frac{1 ⋅ 1 ⋅ 1 ⋅ 1}{3 ⋅ 3 ⋅ 3 ⋅ 3}=\frac{1}{3^4} = (\frac{1}{3})^4$$

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Re: 3 ⋅ 3 ⋅ 3 ⋅ 3/9 ⋅ 9 ⋅ 9 ⋅ 9= &nbs [#permalink] 14 Oct 2017, 14:01
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