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emzy_777
please help:) express the following in the form 2^n 2^70+2^70 answer: 2^71
if this was instead just: x + x what would the answer be?
correct, so now replace x by \(2^{70}\) and what do you get?
not quite, you get two lots of \(2^{70}\) which can be written as:\[2\times2^{70}\]
you can now use the law of exponents to simplify this
e.g.:\[x^a\times x^b=x^{a+b}\]
use the fact that:\[2=2^1\]
its just confusing because i asumed that the answer would be 2^140
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"
think of a simpler example:\[2^3=2\times2\times2\]
so:\[2\times2^3=2\times2\times2\times2=2^4=2^{1+3}\]
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
how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3
same rules apply:\[2^a\times2^b=2^{a+b}\]even if a and b area fractions
you may find this helpful: http://www.mathsisfun.com/exponent.html
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
If you need more background, start with http://www.khanacademy.org/math/algebra/exponents-radicals/v/understanding-exponents it looks like there are quite a few videos, but they are short.