Squaring a Negative Exponent

  • Thread starter Drakkith
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  • #1
Drakkith
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Trying to find out the kinetic energy that a 1kg ball gives the earth if dropped from 100 ft. I just don't know how to square a negative exponent. 4x10^-24 squared is? I was thinking it would be 4x10^-48, but I really don't know. If that is correct, would the result be different if the exponent was an odd number? Like 4x10^-23 squared?
 

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  • #2
Mentallic
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Is it [tex]\left(4\cdot 10^{24}\right)^2[/tex] or [tex]4\cdot \left(10^{24}\right)^2[/tex] ?

Either way, consider the rules [tex](ab)^2=a^2\cdot b^2[/tex] and [tex]\left(a^b\right)^c=a^{bc}[/tex]
 
  • #3
Drakkith
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Should be (4x10^-24)^2
 
  • #4
HallsofIvy
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[itex](a^b)^c= a^{bc}[/itex] so you are multiplying the exponents.

(-24)(2)= -48.

[tex](4\cdot 10^{-24})^2= 4^2\cdot 10^{(2)(-24)}= 16\cdot 10^{-48}[/tex]

If you were writing this in "scientific notation" where the first number is always between 1 and 10, it would be
[tex]1.6\cdot 10^{-47}[/tex]
 
  • #5
Drakkith
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Awesome. Thanks.
 

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