16^7.5÷8^3.5÷2^7.5 =

Question

16^{7.5}÷8^{3.5}÷2^{7.5} =

(A) 2^12 
(B) 2^14
(C) 2^15 
(D) 2^16
(E) 2^27

GMATWhizTeam · Answer

Solution:

We need the value of  16^{7.5} ÷ 8^{3.5} ÷ 2^{7.5}

⇒ 16^{7.5} ÷ \frac{8^{3.5}}{2^{7.5}}

⇒ 16^{7.5} 	imes \frac{2^{7.5}}{8^{3.5}}

⇒ 2^{4	imes 7.5} 	imes \frac{2^{7.5}}{2^{3	imes 3.5}}

⇒ 2^{30} 	imes \frac{2^{7.5}}{2^{10.5}}

⇒ 2^{30+7.5-10.5}

⇒ 2^{27}

Hence the right answer is  Option E .

aggarwal1994 · Answer

GMATWhizTeam , why is this not considered as (16^7.5÷8^3.5)÷(2^7.5)?

Ozzy11100 · Answer

I believe this solution is  incorrect.

The answer is A: 2^12.

The equation becomes 2^30 ÷ 2^10.5 ÷ 2^7.5  ->  30-10.5-7.5 = 12  ->  2^12.

Please correct me if I'm wrong.

stne · Answer

Since both the opertions are division priority is given from left to right.

First: 
  16^{7.5}÷8^{3.5} = \frac {8^{7.5}*2^{7.5}}{ 8^{3.5}} = 8^{4}*2^{7.5}

Second :  \frac{8^4*2^{7.5}}{2^{7.5}} = 8^4 = 2^{12}

Ans-A

Hope it's clear.

bv8562 · Answer

16^7.5÷8^3.5÷2^7.5

(2^4)^7.5÷(2^3)^3.5÷2^7.5

2^30÷2^10.5÷2^7.5 = 2^30-10.5-17.5 = 2^30-18 =  2^12 (A)

Prep Toolkit