One small difference is pretty large

$2^{2014}-2^{2013}$

$=2^{2013}(2)-2^{2013}$

$=2^{2013}(2-1)=\boxed{2^{2013}}$ .

Take a simpler case, such as $2^{3}-2^{2}$ , which equals $2^{2}$ . For any non-zero positive integer $n$ , $2^{n}-2^{n-1}$ = $2^{n-1}$ , so $2^{2014}-2^{2013}$ is $2^{2013}$ .

$2^{2014}$ is simply twice of $2^{2013}$ . Now if we remove $2^{2013}$ from $2^{2014}$ , what we have is, is $2^{2013}$

$2^{2014}-2^{2013} = ?$

$2^{2014} = 2^{2013}+2^{2013}$

$2^{2013}+2^{2013}-2^{2013} = \boxed{2^{2013}}$

Rules of indices: $\boxed{x^{y}=2x^{y-1}}$

You imagine the minimum amount 2 2^4-2^3=? 2^4=16 & 2^3=8 16-8=8 8=2^3 2^4-2^3=2^3 So any count following this pattern So 2^2014 - 2^2013=2^2013

Seemingly, you could half 2 to 2014 powers, since multiplying by two is just doubling (2 squared=4, 2 cubed=8), meaning you could figure this out by knowing what 2 to 2014 powers. Of course, a number that high could be difficult to work with even for what would normally be a simple sum, most notably when using division, being usually quite easy.

$2^{2014} - 2^{2013}$

Factorise out $2^{2013}$ from both terms:

= $2^{2013} (2^{1} - 1)$

Left with final answer:

= $2^{2013} (1) = 2^{2013}$

y^x - y^x-1 = y^x-1

As 2^2014=(2^2013)*2=2^2013+2^2013 That means 2^2014-2^2013=2^2013

k(maybe 2013) is a number and k+1(maybe 2014) is your successor so,
2^(k+1) - 2^k =
2^k*2^1 - 2^k =
2^k + 2^k - 2^k =
2^k

2^2014-2^2013 =2^2013(2-1) =2^2013

Apply equivalent problem of simple units

I dont understand why ppl disscus some problems like that... not abe to solve some problems more difficult ?

2^(n+1) - 2^n = (2^n)(2^1) - 2^n = (2^n)(2-1) = 2^n

2^2013(2-1)=2^2013

x=2013

2^(x+1) - 2^x = 2^x • 2 - 2^x = 2^x • (2 - 1 ) = 2^x

2^x = 2^2013

$\text{Let } 2^{2013} \text{ be }x \\ \text{We know that, }2 \times 2^{2013} = 2^{2014} \ \ \ [a^m \times a^n = a^{m+n}] \\ \therefore 2^{2014} = 2x \\ \Rightarrow 2^{2014} - 2^{2013}= 2x - x =x = \boxed{2^{2013}}$

This one is quite easy but I think some people are over complicating things.

To get 2^{2014} you have to do 2X2^{2013}.

so if we put that in to our equation instead we get :

(2X2^{2013})-2^{2013}=2^{2013}

2^2014 - 2^2013

2^2013(2) -2^2013

2^2013[2-1]

2^2013//

$2^{2014} - 2^{2013} = 2^{2013}(2^{1} - 2^{0}) = 2^{2013}$

So I apparently chose a really roundabout way of solving this, but I got there. Okay, so we know that 2^2013 is just (2^2014)/2. Substitute that in and find a common denominator to subtract, and you get ((2)(2^2014)-(2^2014))/2. So, ((2-1)(2^2014))/2, which simplifies to (2^2014)/2, which we said before was just 2^2013. :)

2^2014=2^2013*2^1

                        Which can be written as

2^2014=2^2013+2^2013

and hence

2^2014-2^2013 = 2^2013+2^2013-2^2013=>

2^2013...

2^2014-2^2013=(2^2013)(2-1)=2^2013

I considered it in the ideas of halves. 2^(n-1) is half of 2^n . Therefore, a whole minus half is half. 2^n - 2^(n-1) = 2^(n-1).

2014 2013 2013 2013 2014 2 =2 + 2 =2 ×2 = 2

2^2013 times 2 is 2^2014, so 2^2014-2^2013 = 2(2^2013)-2^2013 = 2^2013

I do't get it. How come you'll multiply it by 2?

2^n+1 - 2^n is always equal to 2^n .

2^4-2^3=8=2^3 gives the pattern leads to2^2013

2^2014 = 2^2013 x 2 therefore 2(2^2013)-2^2013=X therfore 2^2013=X 2^2013

here X^n - X^(n-1) =X^(n-1) {X-1} =so X become 2, AND n become 2014 =2^2013 * {2 - 1} = 2^2013 ....................ANS

(2p1 2p2013-2 p2013)=2p2013(2-1)=2p2013

It's 2 not 2 to the 2013 power

Just calc unit place digit and eliminate the options

Similar to Victor: i just factored 2^2013(2^2 - 2) = 2^2013

if you calculate (using windows calculator) absolute value for 2^2014 then subtract 2^2013 the answer is 2^2013 !! Tedious big numbers here but with modern computers that can handle them why not nothing like this when i was at school 50 years ago

2^2014 - 2^2013 =2^2013 (2-1) =2^2013 (1) =2^2013

$2^{2014} - 2^{2013} = 2\times(2^{2013} - 2^{2012})$

$2^{2013} - 2^{2012} = 2\times(2^{2012} - 2^{2011})$

$...$

$2^{1} - 2^{0} = 1$

$2^{2014} - 2^{2013} = 2^{2013}\times(1) = 2^{2013}$

2^2014 - 2^2013 = 2^2013(2 - 1) = 2^2013

2^2014 - 2^2013 =2^2013(2) - 2^2013 =2^2013 (2 - 1) = 2^2013

2^2014 is a half from 2^2015 because 2^2015 multiply more than 2^2014 is one number two so 2^2014 is double of 2^2013. 1- 0.5 =0.5 . The answer is 2^2013

2^4 - 2^3 = 16-8=8 (8=2^3)