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emzy_777
 2 years ago
please help:) express the following in the form 2^n
2^70+2^70
answer: 2^71
emzy_777
 2 years ago
please help:) express the following in the form 2^n 2^70+2^70 answer: 2^71

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asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0if this was instead just: x + x what would the answer be?

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

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0you can now use the law of exponents to simplify this

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0e.g.:\[x^a\times x^b=x^{a+b}\]

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0use the fact that:\[2=2^1\]

emzy_777
 2 years ago
Best ResponseYou've already chosen the best response.0its just confusing because i asumed that the answer would be 2^140

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0you 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"

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

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

phi
 2 years ago
Best ResponseYou've already chosen the best response.0first, 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

emzy_777
 2 years ago
Best ResponseYou've already chosen the best response.0how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3

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

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.0you may find this helpful: http://www.mathsisfun.com/exponent.html

phi
 2 years ago
Best ResponseYou've already chosen the best response.0you 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

phi
 2 years ago
Best ResponseYou've already chosen the best response.0If 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.
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