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Simplifying exponential expressions

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Manager
Joined: 23 Jun 2009
Posts: 172
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33

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07 Jun 2016, 17:35
Hi guys,

Could someone explain the following simplifications?

I really don't get them!

7² + 7³ = 7².(7 + 1) = 49.8

4²¹ + 4²¹ + 4²³ = 4²¹(1 + 4 + 16) = 4²¹.(21) = 4²¹(3.7)

I really don't get them!

Appreciate any thoughts on that or material
Math Expert
Joined: 02 Aug 2009
Posts: 8618

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07 Jun 2016, 21:11
1
felippemed wrote:
Hi guys,

Could someone explain the following simplifications?

I really don't get them!

7² + 7³ = 7².(7 + 1) = 49.8

4²¹ + 4²¹ + 4²³ = 4²¹(1 + 4 + 16) = 4²¹.(21) = 4²¹(3.7)

I really don't get them!

Appreciate any thoughts on that or material

Hi

$$7^2 + 7^3 = 7*7+7*7*7 ... 7*7$$ is common in two terms, so move it out ...
$$7*7*(1+7) = 49 *8$$..

$$4^{21}+4^{21}+4^{23} = 4^{21}(1+1+4^{23-21} = 4^{21}(1+1+4^2) = 4^{21}(18)$$...... take out common 4^21
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Manager
Joined: 23 Jun 2009
Posts: 172
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33

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09 Jun 2016, 05:59
Quote:
72+73=7∗7+7∗7∗7...7∗772+73=7∗7+7∗7∗7...7∗7 is common in two terms, so move it out ...

Saved my life!

Thanks a lot
Re: Simplifying exponential expressions   [#permalink] 09 Jun 2016, 05:59