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# If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =  [#permalink]

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13 Mar 2019, 01:08
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Difficulty:

25% (medium)

Question Stats:

75% (02:24) correct 25% (02:25) wrong based on 53 sessions

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If $$4^x = 1024$$, then $$4^{x + 1}*5^{x - 1} =$$

A. 10^6

B. 5^4*10^5

C. 4^4*10^5

D. 5^4*10^4

E. 4^4*10^4

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Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =  [#permalink]

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13 Mar 2019, 03:50
Bunuel wrote:
If $$4^x = 1024$$, then $$4^{x + 1}*5^{x - 1} =$$

A. 10^6

B. 5^4*10^5

C. 4^4*10^5

D. 5^4*10^4

E. 4^4*10^4

$$4^x = 1024$$
x=5
so $$4^{x + 1}*5^{x - 1} =$$
4^6*5^4
or say
2^12*5^4
10^4*2^8
10^4*4^4
IMO E
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Joined: 03 Mar 2019
Posts: 2
Re: If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =  [#permalink]

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26 Mar 2019, 04:24
Archit3110

How do you do the last three steps?
2^12*5^4
10^4*2^8
10^4*4^4
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =  [#permalink]

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26 Mar 2019, 07:48
Archit3110

How do you do the last three steps?
2^12*5^4
10^4*2^8
10^4*4^4

well its just simplfying the expression
4^6*5^4
4^6= 2^2*6;2^12
so
2^12*5^4
10^4*2^8 ; multiply 2^4*5^4
2^8 can be written as 4^4 since 2^2= 4
so
10^4*2^8 = 10^4*4^4

hope this helps
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Re: If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =  [#permalink]

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27 Mar 2019, 19:03
Bunuel wrote:
If $$4^x = 1024$$, then $$4^{x + 1}*5^{x - 1} =$$

A. 10^6

B. 5^4*10^5

C. 4^4*10^5

D. 5^4*10^4

E. 4^4*10^4

Simplifying we have:

2^(2x) = 2^10

2x = 10

x = 5

So we have:

4^6 x 5^4

2^12 x 5^4 = 2^8 x 2^4 x 5^4 = 2^8 x 10^4 = 4^4 x 10^4

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Re: If 4^x = 1024, then 4^(x + 1)*5^(x - 1) =   [#permalink] 27 Mar 2019, 19:03
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