How do you square a negative exponent for kinetic energy calculation?

In summary, the conversation discusses finding the kinetic energy of a 1kg ball dropped from 100 ft and how to square a negative exponent. The correct way is to multiply the exponents, resulting in a squared value of 4x10^-48. This rule also applies to scientific notation, where the first number is between 1 and 10.
  • #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
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
Should be (4x10^-24)^2
 
  • #4
[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
Awesome. Thanks.
 

What does it mean to square a negative exponent?

Squaring a negative exponent means to raise the number with the negative exponent to the power of 2, or to multiply it by itself.

What is the rule for squaring a negative exponent?

The rule for squaring a negative exponent is to first change the sign of the exponent to positive, then raise the number to the power of 2.

Why does squaring a negative exponent result in a positive number?

This is because when we square a number, we are multiplying it by itself, which cancels out the negative sign of the exponent and results in a positive value.

Can we square any negative exponent?

Yes, we can square any negative exponent as long as the base number is a real number.

Can we use the same rule for higher powers of negative exponents?

No, the rule for squaring a negative exponent cannot be applied to higher powers, such as cubing or to the power of 4. Each power has its own specific rule that must be followed.

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