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# (8^16)+(16^13)+(4^24) = ?

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Manager
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28 Mar 2014, 21:46
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45% (medium)

Question Stats:

67% (02:31) correct 33% (01:27) wrong based on 114 sessions

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(8^16)+(16^13)+(4^24) = ?

A. (4)*(2^29+1)
B. (6)*(2^48)
C. (9)*(2^49)
D. (28)*(2^53)
E. 2^148
[Reveal] Spoiler: OA

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28 Mar 2014, 22:08
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(8^16)+(16^13)+(4^24)

((2^3)^16)+((2^4)^13)+((2^2)^24)

(2^48)+(2^52)+(2^48)

(2^48)+((2^48)*(2^4))+(2^48)

(2^48)(1+1+2^4)

(2^48)(2+2^4)

(2^48)*2*(1+2^3)

(2^49)(9)

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28 Mar 2014, 22:21
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?
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28 Mar 2014, 22:26
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royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?[/quote]

(a^m)(a^n) = a^(m+n)

Eg. 2^3.2^2 = 2^5

However
a^m + a^n is not a^(m+n)
2^3 + 2^2 is not 2^5 (i.e 8 + 4 is not 32)
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30 Mar 2014, 21:53
royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?

I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)

So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.

Here's how my brain works with this one,

Step 1: Recognize a common base.

(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)

Step 2: Recognize the factor and pull out of the equation.

= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)

(2^48)(18) = (2^48)(2)(9) = (2^49)(9)

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31 Mar 2014, 19:11
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$$8^{16} = 2^{48}$$

$$16^{13} = 2^{52}$$

$$4^{24} = 2^{48}$$

$$2^{48} + 2^{52} + 2^{48}$$

$$= 2^{49} + 2^{52}$$

$$= 2^{49} (1+8)$$

$$= 9 * 2^{49}$$

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31 Mar 2014, 21:18
royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?[/quote]

You cannot just add exponents when you sum the same bases, in this case 2. If it was multiplying you could do so. Another rule which is useful here is that 2^48+2^48=2^49. Adding as much times as base (the same) and same exponent gives us the same base with +1 in exponent
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01 Apr 2014, 02:12
royQV wrote:

I do understand that C is the correct choice but can you please explain why e is wrong?

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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22 Aug 2015, 20:28
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Re: (8^16)+(16^13)+(4^24) = ?   [#permalink] 22 Aug 2015, 20:28
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