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please help:) express the following in the form 2^n
2^70+2^70
answer: 2^71
 one year ago
 one year ago
please help:) express the following in the form 2^n 2^70+2^70 answer: 2^71
 one year ago
 one year ago

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asnaseerBest ResponseYou've already chosen the best response.0
if this was instead just: x + x what would the answer be?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
correct, so now replace x by \(2^{70}\) and what do you get?
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
not quite, you get two lots of \(2^{70}\) which can be written as:\[2\times2^{70}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
you can now use the law of exponents to simplify this
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
e.g.:\[x^a\times x^b=x^{a+b}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
use the fact that:\[2=2^1\]
 one year ago

emzy_777Best ResponseYou've already chosen the best response.0
its just confusing because i asumed that the answer would be 2^140
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
you have 2 to the power of 1 times 2 to the power of 70. so, using the law of exponents I showed above, the answer should be 2 to the power of "1 plus 70"
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
think of a simpler example:\[2^3=2\times2\times2\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
so:\[2\times2^3=2\times2\times2\times2=2^4=2^{1+3}\]
 one year ago

phiBest ResponseYou've already chosen the best response.0
first, this is a special case.. it is not a general rule but 2^70 * 2^70 you add exponents to get 2^140 but here they are adding 2^70 + 2^70 you can factor out 2^70 to get 2^70(1+1) or 2^70 * 2^1 or 2^71 but notice this does NOT WORK: 2^70 + 2^70 + 2^70 you factor out 2^70 to get 2^70(1+1+1)= 3* 2^70 and that is all we can do
 one year ago

emzy_777Best ResponseYou've already chosen the best response.0
how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
same rules apply:\[2^a\times2^b=2^{a+b}\]even if a and b area fractions
 one year ago

asnaseerBest ResponseYou've already chosen the best response.0
you may find this helpful: http://www.mathsisfun.com/exponent.html
 one year ago

phiBest ResponseYou've already chosen the best response.0
you could say 2^1/3+2^1/3+2^1/3+2^1/3 is the same as 4* 2^(1/3) now it happens that 4 is 2^2 so you write it as 2^2 * 2^(1/3) now use the add exponent rule : when multiplying two numbers with the SAME BASE, add their exponents
 one year ago

phiBest ResponseYou've already chosen the best response.0
If you need more background, start with http://www.khanacademy.org/math/algebra/exponentsradicals/v/understandingexponents it looks like there are quite a few videos, but they are short.
 one year ago
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