An example illustrating the laws of exponents

In summary: For large values of 2.In summary, the well-known rule for multiplying numbers raised to powers does not always work. The rule only applies when the bases are the same. Furthermore, the rule only applies when the numbers have the same exponent.
  • #1
fourier jr
765
13
Using the well-known rule for multiplying numbers raised to powers:

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

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

If you can think of a better way I'd sure like to see it! :biggrin:
 
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  • #2
Wow, that is so easy! I never though about it like that before. I always used to do it the hard way.
 
  • #3
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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  • #4
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.

[tex]3^{3/2}9^{6/7} = 34.1668 \neq (3*9)^{\frac{3+6}{2+7}} = 27[/tex]
 
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  • #5
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.
 
  • #6
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
 
  • #7
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!
 
  • #8
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.
 
  • #9
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 [tex]\lim_{8\rightarrow 9}\sqrt{8} = 3[/tex]
 
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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:

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

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

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 [tex]\frac{16}{64}[/tex] by canceling out the sixes.
 
  • #21
jimmysnyder said:
It reminds me of simplifying [tex]\frac{16}{64}[/tex] 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 [tex]\lim_{8\rightarrow 9}\sqrt{8} = 3[/tex]

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

[tex]2\approx3[/tex]
For large values of 2.
 

FAQ: An example illustrating the laws of exponents

What are the basic laws of exponents?

The basic laws of exponents are:
- Product Rule: when multiplying two powers with the same base, add the exponents
- Quotient Rule: when dividing two powers with the same base, subtract the exponents
- Power Rule: when raising a power to a power, multiply the exponents
- Zero Rule: any number (except 0) raised to the power of 0 is equal to 1
- Negative Rule: a negative exponent indicates the reciprocal of the number raised to the positive exponent

How do these laws apply to real-life situations?

These laws of exponents are commonly used in scientific fields such as physics, chemistry, and biology. They are used to simplify and solve complex equations involving large or small numbers. For example, in chemistry, the molar concentration of a solution can be calculated using the power rule to raise the number of moles to a power. In physics, these laws are used to calculate the growth and decay of radioactive elements.

Can you provide an example illustrating the product rule?

One example of the product rule is (2^3)(2^5) = 2^(3+5) = 2^8 = 256. In this case, we are multiplying two powers with the same base (2) and adding the exponents (3 and 5) to get the final exponent (8).

How does the zero rule work?

The zero rule states that any number (except 0) raised to the power of 0 is equal to 1. For example, 5^0 = 1, 10^0 = 1, and (-3)^0 = 1. This rule is important in simplifying equations and solving problems involving exponents.

Why is the negative rule important?

The negative rule is important because it allows us to work with negative exponents, which often arise in real-life situations. For instance, in physics, negative exponents can represent decaying quantities. The reciprocal property of negative exponents helps us to simplify and solve these types of equations.

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