Which of the following is the approximation of

Question

Which of the following is the approximation of  \frac{4^4+8^6}{4^8+16^8} ?

A.  2^{-12}  
B.  2^{-14}  
C.  2^{-16}  
D.  2^{12}  
E.  2^{14}

ScottTargetTestPrep · Answer

We can start by prime factorizing each term in the given expression:

4^4 = (2^2)^4 = 2^8

8^6 = (2^3)^6 = 2^18

4^8 = (2^2)^8 = 2^16

16^8 = (2^4)^8 = 2^32

Putting these values back into the given expression, we have:

(2^8 + 2^18)/(2^16 + 2^32)

We can factor out a 2^8 from the numerator and a 2^16 from the denominator, and we have:

/

(1 + 2^10)/

Since the 1s are quite small compared to the other values, we can ignore them, and we have:

2^10/(2^8 x 2^16) = 2^10/2^24 = 2^-14

Answer: B

MathRevolution · Answer

==> Because of the word “approximation”, you get  (4^4+8^6)/(4^8+16^8)= 8^6/16^8 . 
Also, from  8^6/16^8 =(2^3)^6/(2^4)^8=2^1^8/2^3^2=2^1^8^-^3^2=2^-^1^4 , the answer is B.

Answer: B

Nipungupta9081 · Answer

IMO B

i ignored 1 because we need to find the approx value.

Abhishek009 · Answer

(4^4+8^6)/(4^8+16^8 )

Or,  \frac{(2^8+2^{18})}{(2^{16}+2^{32}} )

Or,  \frac{2^8(1 + 2^{10})}{2^{16}(1 + 2^{16})}

Or,  \frac{( 2^{10})}{2^{8}(2^{16})}   {Approximately}

Or,  \frac{( 2^{10})}{(2^{24})}

Or,  2^{-14} , Answer will clearly be (B)

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Which of the following is the approximation of

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Which of the following is the approximation of

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