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how to solve 4^4 quick

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IamWeezel
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how to solve 4^4 quick [#permalink] New post   18 Nov 2016, 04:27
hey guys,

is there something like a trick to solve problems like 4^4 quickly.

or something like 625=x^y
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Re: how to solve 4^4 quick [#permalink] New post   18 Nov 2016, 13:00
IamWeezel wrote:
hey guys,

is there something like a trick to solve problems like 4^4 quickly.

or something like 625=x^y


\(4^4 = 2^8 = 256\)

625=x^y

Or, \(5^4 = x^y\) , so x = 5 & y = 4
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Re: how to solve 4^4 quick [#permalink] New post   19 Nov 2016, 10:42
Yes, you can turn 4^4 into (2^2) ^4 = 2^8

Or if you want to mentally multiply, it's 4*4 = 16
16*4 =64

64 *4 -- this one gets a little bit more complicated.

Here's how you tackle:

Round 64 to the more comfortable number 60 -- and multiply 60 * 4 = 240

Now we need to add to this 240 -- how much?

Since we reduced 64 down to 60 by an amount of 4, we need to now take that 4 and multiply it by 4 -- that's 16.

Add this 16 back to the 240 and you get 240 + 16 = 256
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Re: how to solve 4^4 quick [#permalink] New post   21 Nov 2016, 17:00
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IamWeezel wrote:
hey guys,
or something like 625=x^y


For this one, if I wasn't sure, I'd start by using a factor tree to factor 625. You end up finding that 625 = 5*5*5*5, so x = 5 and y = 4. (Or, x = 25 and y = 2! There are multiple solutions here... unless you know that x has to be prime.)
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Re: how to solve 4^4 quick [#permalink] New post   21 Nov 2016, 18:53
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IamWeezel wrote:
hey guys,

is there something like a trick to solve problems like 4^4 quickly.

or something like 625=x^y


The best would be to multiply and get your answer ...
A slightly better method depending on numbers would be...
1) 29^2
29^2=(30-1)^2=30^2+1^2-2*30*1=900+1-60=841..
2) similarly 31^2=(30+1)^2

Now for 4^4=(4^2)^2=16^2=(10+6)^2=10^2+6^2+2*10*6=100+36+120=256..
Or (20-4)^2=20^2+4^2-2*20*4=400+16-160=240+16=256

So you can ease your squares in some way..
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Re: how to solve 4^4 quick [#permalink]
21 Nov 2016, 18:53
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Bunuel
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