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1. asnaseer

if this was instead just: x + x what would the answer be?

2. anonymous

2x

3. asnaseer

correct, so now replace x by $$2^{70}$$ and what do you get?

4. anonymous

4^70...

5. asnaseer

not quite, you get two lots of $$2^{70}$$ which can be written as:$2\times2^{70}$

6. asnaseer

you can now use the law of exponents to simplify this

7. asnaseer

e.g.:$x^a\times x^b=x^{a+b}$

8. asnaseer

use the fact that:$2=2^1$

9. anonymous

ok i kinda get it

10. asnaseer

great! :)

11. anonymous

its just confusing because i asumed that the answer would be 2^140

12. asnaseer

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"

13. asnaseer

think of a simpler example:$2^3=2\times2\times2$

14. asnaseer

so:$2\times2^3=2\times2\times2\times2=2^4=2^{1+3}$

15. phi

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

16. anonymous

how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3

17. asnaseer

same rules apply:$2^a\times2^b=2^{a+b}$even if a and b area fractions

18. asnaseer

you may find this helpful: http://www.mathsisfun.com/exponent.html

19. phi

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

20. phi