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Math Expert V
Joined: 02 Sep 2009
Posts: 60546
What is the value of 4^5+4^7?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 76% (00:40) correct 24% (00:52) wrong based on 127 sessions

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What is the value of $$4^5+4^7$$?

(A) $$4^{12}$$
(B) $$4^{35}$$
(C) $$17(4^5)$$
(D) $$8^{12}$$
(E) $$7(4^5)$$

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Director  P
Joined: 16 Jan 2019
Posts: 534
Location: India
Concentration: General Management
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What is the value of 4^5+4^7?  [#permalink]

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$$4^5+4^7=4^5(1+4^2)=4^5(1+16)=17(4^5)$$

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Intern  B
Joined: 31 Aug 2019
Posts: 3
Re: What is the value of 4^5+4^7?  [#permalink]

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4^5 + 4^7

First we can factor out 4^5 and we are left with;

4^5(1 + 4^2)

Then we can compute 4^2, which is 16.

4^5(1 + 16)

the result is;

4^5(17)
Intern  B
Joined: 28 Jan 2019
Posts: 39
GMAT 1: 730 Q47 V42
Re: What is the value of 4^5+4^7?  [#permalink]

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Whenever you have addition or subtraction of same bases raised to different exponents, try factoring out the least common exponent.

4^5+4^7 = 4^5(1+4^2)
=4^5(17)
Target Test Prep Representative V
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Joined: 14 Oct 2015
Posts: 9065
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Re: What is the value of 4^5+4^7?  [#permalink]

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Bunuel wrote:
What is the value of $$4^5+4^7$$?

(A) $$4^{12}$$
(B) $$4^{35}$$
(C) $$17(4^5)$$
(D) $$8^{12}$$
(E) $$7(4^5)$$

Simplifying, we have:

4^5(1 + 4^2) = 4^5(17)

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Intern  B
Joined: 22 Jun 2017
Posts: 8
Re: What is the value of 4^5+4^7?  [#permalink]

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Someone could explain me in details how is the process of factoring out the least common of an exponent?
I tried to figure out by myself but didn't find any theoretical material Re: What is the value of 4^5+4^7?   [#permalink] 03 Dec 2019, 16:47
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# What is the value of 4^5+4^7?   