Math Destroyer 2011 Test 2 Question 11

[flin5845]

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Simplify 4^9 / [ 8x (16^4 - 2 x 8^4)]. ANS: 4/7

I do not understand the explanation but this is what I was doing:
- Made all the bases in terms of powers of 2 and got

2^18/ [2^3(2^16 - 2 x 2^12)] I multiplied the 2 and 2^13
2^18/ [2^3(2^16 - 2^13)] I distributed the 2^3
2^18/ [ 2^19 - 2^16] But now this is where I do not know what to do.

How can I solve these problems fast? I know they are not hard....I just get confused...

Thanks guys...

 

[rockclock]

Simplify 4^9 / [ 8x (16^4 - 2 x 8^4)]. ANS: 4/7

I do not understand the explanation but this is what I was doing:
- Made all the bases in terms of powers of 2 and got

2^18/ [2^3(2^16 - 2 x 2^12)] I multiplied the 2 and 2^13
2^18/ [2^3(2^16 - 2^13)] I distributed the 2^3
2^18/ [ 2^19 - 2^16] But now this is where I do not know what to do.

How can I solve these problems fast? I know they are not hard....I just get confused...

Thanks guys...

distributing was the wrong way to go. you should have factored 2^13 out...

2^18 / [2^3 * 2^13 * (2^3 - 1)]
= 2^2 / (2^3 - 1)
= 4 / 7

...or you could factor 2^16 out in your last line and do the same thing, though that's an additional step