# An example illustrating the laws of exponents

1. Apr 26, 2007

### fourier jr

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!

Last edited: Apr 26, 2007
2. Apr 26, 2007

### G01

Wow, that is so easy! I never though about it like that before. I always used to do it the hard way.

3. Apr 26, 2007

### Cyrus

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 cant just add exponents like that with different basii.

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

Last edited: Apr 26, 2007
4. Apr 26, 2007

### mattmns

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.

$$3^{3/2}9^{6/7} = 34.1668 \neq (3*9)^{\frac{3+6}{2+7}} = 27$$

Last edited: Apr 26, 2007
5. Apr 27, 2007

### leright

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

6. Apr 27, 2007

### Cyrus

basii

more text

7. Apr 27, 2007

### fourier jr

That's why it's so funny!!! You get the right answer, but for the wrong reasons!

8. Apr 27, 2007

### leright

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

9. Apr 27, 2007

### fourier jr

that's what's so funny though, it's totally wrong except the answer is correct anyway

10. Apr 27, 2007

### Cyrus

Ha ha?

11. Apr 27, 2007

### cristo

Staff Emeritus
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. Apr 27, 2007

### Physics_wiz

I guess I need to get out more.

13. Apr 27, 2007

### fourier jr

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

Last edited: Apr 27, 2007
14. Apr 27, 2007

### leright

incorrect.

or are you joking?

15. Apr 27, 2007

### Cyrus

Now thats funny :rofl:

16. Apr 27, 2007

### leright

I smirked.

17. Apr 27, 2007

### leright

I take it my sarcasm/joke meter is defunct?

18. Jan 8, 2009

### melaws24

33/2 +96/7=33/2 +312/7
= only which is 11.771552

Last edited by a moderator: Jan 8, 2009
19. Jan 8, 2009

### rootX

Why not just ...

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

20. Jan 8, 2009

### Jimmy Snyder

It reminds me of simplifying $$\frac{16}{64}$$ by canceling out the sixes.

21. Jan 8, 2009

### Pythagorean

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. Jan 8, 2009

### moe darklight

O god... I actually chuckled out loud.

I need to get out more.

23. Jan 13, 2009

### LennoxLewis

A broken clock is still correct twice a day.

24. Jan 13, 2009

### NeoDevin

I always liked

$$2\approx3$$
For large values of 2.