Please help (8^2)(3^3)(2^4)/(96^2) GMAC Problem

KingTmo wrote:Please help with this as the GMAC problems have no solution. I know its easy but, I still need help!!! Thanks

(8^2)(3^3)(2^4)/(96^2)
8^2= (2*2*2)^2=(2^3)^2=2^6 (since (a^m)^n=a^mn)

96^2=(2*2*2*2*2*3)^2=(2^5*3)^2=2^10* 3^2

now (8^2)(3^3)(2^4)/(96^2)
(2^6)(3^3)(2^4)/2^10* 3^2 (a^b+a^c =a(b+c))
2^10*3^3/2^10* 3^2
=3

Please help (8^2)(3^3)(2^4)/(96^2) GMAC Problem

hi........
it would do you a world of good to memorize squares/cubes of numbers at least up to 20

8^2=8*8=64
3^3=3*3=27
2^4=2*2*2*2=16
96^2=96*96
simply solve to get the the answer=3

also remember
2^2=4
2^3=8
2^4=16
2^5=32
2^6=64
can you see the relation ?

For solving this question you should not multiply the numbers. There is quick way and smart way(if you are not able to do it quick)

Quick way : As intellijat mentioned above. However if you do not remember the square of the number then do not make the mistake of mutiplying (8^2)(3^3)(2^4)/(96^2) .

For this sort of quetion you can simply reduce it to simplest fraction and and divide in parts. EX - 8^2 / 2^2

8 * 8 / 2 * 2 = 4 * 4 = 16.

You can do the same for the actual problem as well.

its simple....first check the highest numbers.....8^2 and 96^2

now 96/8=12, so in d denominator we have 12^2 instead of 96 if we factor out 8 from the numerator

2^4 = 4^2 now that goes very well with 12^2 in the denom.........giving us 3^2
So we are now left with

3^3/ 3^2 = 3 very simple.......voila!! Cheers

For this problem easiest way was to simplify using the exponent rule:
(8^2)(3^3)(2^4)/(96^2)

This can be rewritten in powers of 2 by the following, 96 has the prime factorization of 2^5 x 3:
[(2^3)^2 } (3^3)(2^4)/(2^5*3)^2

Now combine like terms and powers:
2^(6+4) (3^3)/(2^10*3^2)

Here the 2^10 can cancel out and we're left with:
3^3/3^2
which leaves us with answer of 3