An example illustrating the laws of exponents

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The forum discussion centers around the application of the exponent multiplication rule: u^{\frac{a}{b}}v^{\frac{c}{d}} = (uv)^{\frac{a+c}{b+d}}. Participants critique the validity of this rule, noting that it only applies when the bases are the same and that it fails for many cases, particularly when a or c equals zero. The conversation highlights the humorous aspect of deriving correct answers through incorrect reasoning, emphasizing that while the formula may yield correct results in specific instances, it lacks general applicability.

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Using the well-known rule for multiplying numbers raised to powers:

u^{\frac{a}{b}}v^\frac{c}{d}} = (uv)^{\frac{a+c}{b+d}},

3^{2/3}9^{7/6} = (3*9)^{\frac{2+7}{3+6}} = 27

If you can think of a better way I'd sure like to see it! :biggrin:
 
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Wow, that is so easy! I never though about it like that before. I always used to do it the hard way.
 
Wont work if a or c is zero though. Probably why its not a rule.

And, that rule only applies when they have the same base. You can't just add exponents like that with different basii.

Uh yeah, your formula isint working for a lot of numbers.
 
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Yeah it looks like it is not as general as he stated it. Looks like an infinite number of examples that it does not work for.

Consider flipping the fractions.

3^{3/2}9^{6/7} = 34.1668 \neq (3*9)^{\frac{3+6}{2+7}} = 27
 
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cyrusabdollahi said:
Wont work if a or c is zero though. Probably why its not a rule.

And, that rule only applies when they have the same base. You can't just add exponents like that with different basii.

Uh yeah, your formula isint working for a lot of numbers.

Not only are the bases different but a/c + b/d is not equal to (a+b)/(c+d). :confused: I think the OP is referring to a completely different "rule" than you are referring to.
 
leright said:
Not only are the bases different but a/c + b/d is not equal to (a+b)/(c+d). :confused: I think the OP is referring to a completely different "rule" than you are referring to.

basii

more text
 
leright said:
Not only are the bases different but a/c + b/d is not equal to (a+b)/(c+d). :confused:

That's why it's so funny! :rolleyes: You get the right answer, but for the wrong reasons!
 
fourier jr said:
That's why it's so funny! :rolleyes: You get the right answer, but for the wrong reasons!

:rolleyes: As mentioned above, that only works in like one case. I don't see the point of this thread.
 
leright said:
:rolleyes: As mentioned above, that only works in like one case. I don't see the point of this thread.

that's what's so funny though, it's totally wrong except the answer is correct anyway
 
  • #10
Ha ha? :confused:
 
  • #11
fourier jr said:
that's what's so funny though, it's totally wrong except the answer is correct anyway

Wow.. if you find that funny you need to get out more.

Seriously though, there are infinitely many "formulae" one can construct that are incorrect but hold coincidentally give the correct answer in one or two cases. However, there is no merit to be had in discussing such "formulae".
 
  • #12
cristo said:
Wow.. if you find that funny you need to get out more.

I guess I need to get out more.
 
  • #13
cristo said:
Wow.. if you find that funny you need to get out more.

Seriously though, there are infinitely many "formulae" one can construct that are incorrect but hold coincidentally give the correct answer in one or two cases. However, there is no merit to be had in discussing such "formulae".

no, I think if you don't find it funny then YOU should get out more... & lighten up. But on the other hand, it isn't the funniest math joke I know, which is still \lim_{8\rightarrow 9}\sqrt{8} = 3
 
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  • #14
cyrusabdollahi said:
basii

more text

incorrect.

or are you joking?
 
  • #15
Now that's funny :smile:
 
  • #16
cristo said:
Wow.. if you find that funny you need to get out more.

Seriously though, there are infinitely many "formulae" one can construct that are incorrect but hold coincidentally give the correct answer in one or two cases. However, there is no merit to be had in discussing such "formulae".

I smirked.
 
  • #17
cyrusabdollahi said:
Now that's funny :smile:

I take it my sarcasm/joke meter is defunct?
 
  • #18
33/2 +96/7=33/2 +312/7
= only which is 11.771552
 
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  • #19
fourier jr said:
Using the well-known rule for multiplying numbers raised to powers:

u^{\frac{a}{b}}v^\frac{c}{d}} = (uv)^{\frac{a+c}{b+d}},

3^{2/3}9^{7/6} = (3*9)^{\frac{2+7}{3+6}} = 27

If you can think of a better way I'd sure like to see it! :biggrin:

Why not just ...

ua/bvc/d = ua/buk*c/d
=ua/b+kc/d

:confused:
 
  • #20
It reminds me of simplifying \frac{16}{64} by canceling out the sixes.
 
  • #21
jimmysnyder said:
It reminds me of simplifying \frac{16}{64} by canceling out the sixes.

this one I'd do to my professors.

I'd be scared to do the OP's joke because the uptight ones might think I'm serious :/
 
  • #22
fourier jr said:
But on the other hand, it isn't the funniest math joke I know, which is still \lim_{8\rightarrow 9}\sqrt{8} = 3

O god... I actually chuckled out loud.

I need to get out more.
 
  • #23
A broken clock is still correct twice a day.
 
  • #24
I always liked

2\approx3
For large values of 2.
 

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