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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

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  1. asnaseer
    • 2 years ago
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    if this was instead just: x + x what would the answer be?

  2. emzy_777
    • 2 years ago
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    2x

  3. asnaseer
    • 2 years ago
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    correct, so now replace x by \(2^{70}\) and what do you get?

  4. emzy_777
    • 2 years ago
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    4^70...

  5. asnaseer
    • 2 years ago
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    not quite, you get two lots of \(2^{70}\) which can be written as:\[2\times2^{70}\]

  6. asnaseer
    • 2 years ago
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    you can now use the law of exponents to simplify this

  7. asnaseer
    • 2 years ago
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    e.g.:\[x^a\times x^b=x^{a+b}\]

  8. asnaseer
    • 2 years ago
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    use the fact that:\[2=2^1\]

  9. emzy_777
    • 2 years ago
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    ok i kinda get it

  10. asnaseer
    • 2 years ago
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    great! :)

  11. emzy_777
    • 2 years ago
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    its just confusing because i asumed that the answer would be 2^140

  12. asnaseer
    • 2 years ago
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    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
    • 2 years ago
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    think of a simpler example:\[2^3=2\times2\times2\]

  14. asnaseer
    • 2 years ago
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    so:\[2\times2^3=2\times2\times2\times2=2^4=2^{1+3}\]

  15. phi
    • 2 years ago
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    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. emzy_777
    • 2 years ago
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    how would you do it with fractions though? like 2^1/3+2^1/3+2^1/3+2^1/3

  17. asnaseer
    • 2 years ago
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    same rules apply:\[2^a\times2^b=2^{a+b}\]even if a and b area fractions

  18. asnaseer
    • 2 years ago
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    you may find this helpful: http://www.mathsisfun.com/exponent.html

  19. phi
    • 2 years ago
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    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
    • 2 years ago
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    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.

  21. emzy_777
    • 2 years ago
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    thanks alot :)

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