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

Question

A. (4)*(2^29+1)
B. (6)*(2^48)
C. (9)*(2^49)
D. (28)*(2^53)
E. 2^148

MacFauz · Answer

(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

royQV · Answer

Dear MacFauz

Answer is C

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

abid1986 · Answer

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

(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)

dbiersdo · Answer

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

PareshGmat · Answer

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

Temurkhon · Answer

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

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

Bunuel · Answer

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

lalania1 · Answer

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.

bumpbot · Answer

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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