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

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

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New post 28 Mar 2014, 20:46
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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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Re: Exponent Rule [#permalink]

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New post 28 Mar 2014, 21:08
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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)

Answer is C
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Re: Exponent Rule [#permalink]

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New post 28 Mar 2014, 21:21
Dear MacFauz

Answer is C[/quote]

I do understand that C is the correct choice but can you please explain why e is wrong?
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Re: Exponent Rule [#permalink]

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New post 28 Mar 2014, 21:26
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royQV wrote:
Dear MacFauz

Answer is C


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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Re: Exponent Rule [#permalink]

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New post 30 Mar 2014, 20:53
royQV wrote:
Dear MacFauz

Answer is C

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)

Step 3: Recognize this is not an answer and adapt.

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

Answer is C. :-D
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Re: (8^16)+(16^13)+(4^24) = ? [#permalink]

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New post 31 Mar 2014, 18:11
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\(8^{16} = 2^{48}\)

\(16^{13} = 2^{52}\)

\(4^{24} = 2^{48}\)

Adding the above three terms

\(2^{48} + 2^{52} + 2^{48}\)

\(= 2^{49} + 2^{52}\)

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

\(= 9 * 2^{49}\)

= Answer = C
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Re: Exponent Rule [#permalink]

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New post 31 Mar 2014, 20:18
royQV wrote:
Dear MacFauz

Answer is C


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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Re: Exponent Rule [#permalink]

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New post 01 Apr 2014, 01:12
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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Re: (8^16)+(16^13)+(4^24) = ? [#permalink]

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Re: (8^16)+(16^13)+(4^24) = ? [#permalink]

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New post 24 Nov 2016, 09:35
In this question, the trick is to do the below

2^48 + 2^48 = 2^49

I did not know the above was possible before. I will remember this for future questions.
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Re: (8^16)+(16^13)+(4^24) = ?   [#permalink] 24 Nov 2016, 09:35
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