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# 3^5 + 1/3^5 =

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Math Expert
Joined: 02 Sep 2009
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13 Mar 2018, 06:47
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15% (low)

Question Stats:

90% (00:50) correct 10% (00:59) wrong based on 88 sessions

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$$3^5 + \frac{1}{3^5} =$$

A. 1

B. 3

C. $$\frac{3^6 - 1}{3}$$

D. $$\frac{3^{10} + 1}{3^5}$$

E. $$\frac{3^{25}}{3^5 + 1}$$

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Re: 3^5 + 1/3^5 =  [#permalink]

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13 Mar 2018, 06:57
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Re: 3^5 + 1/3^5 =  [#permalink]

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13 Mar 2018, 07:09
1
D. Because 3^5 x 3^5 = 3^10
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Re: 3^5 + 1/3^5 =  [#permalink]

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13 Mar 2018, 07:19
Bunuel wrote:
$$3^5 + \frac{1}{3^5} =$$

A. 1

B. 3

C. $$\frac{3^6 - 1}{3}$$

D. $$\frac{3^{10} + 1}{3^5}$$

E. $$\frac{3^{25}}{3^5 + 1}$$

Clean (D) $$\frac{3^{10} + 1}{3^5}$$
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Re: 3^5 + 1/3^5 =  [#permalink]

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13 Mar 2018, 11:06
a+1/a= (a^2+1)/a
Hence D = {3^(5+5) +1}/(3^5) = (3^10 +1)/(3^5)
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13 Mar 2018, 12:49
Bunuel wrote:
$$3^5 + \frac{1}{3^5} =$$

A. 1

B. 3

C. $$\frac{3^6 - 1}{3}$$

D. $$\frac{3^{10} + 1}{3^5}$$

E. $$\frac{3^{25}}{3^5 + 1}$$

$$a^{n} * a^{m} = a^{(n+m)}$$

$$3^5 + \frac{1}{3^5} =$$

$$(\frac{3^5}{1}*\frac{3^5}{3^5})+(\frac{1}{3^5}*\frac{3^5}{3^5})=$$

$$\frac{3^5*3^5}{3^5}+\frac{1}{3^5}=$$

$$\frac{3^{(5+5)}}{3^5} + \frac{1}{3^5}=$$

$$\frac{3^{10} + 1}{3^5}$$

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Re: 3^5 + 1/3^5 =  [#permalink]

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14 Mar 2018, 16:03
Bunuel wrote:
$$3^5 + \frac{1}{3^5} =$$

A. 1

B. 3

C. $$\frac{3^6 - 1}{3}$$

D. $$\frac{3^{10} + 1}{3^5}$$

E. $$\frac{3^{25}}{3^5 + 1}$$

Getting common denominators we have:

(3^5 x 3*5)/3^5 + 1/3^5

3^10/3^5 + 1/3^5 = (3^10 + 1)/3^5

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Re: 3^5 + 1/3^5 =   [#permalink] 14 Mar 2018, 16:03
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