Exponents with fractions and irrational numbers

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vivia

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Nov 22, 2020
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Um hello earthlings!
I'm having a bit of problem with exponents. Not like [6[2], but more like[5[/6/97] or [675[/1.66666666666666666 (to infinity)]. Could someone help me? I just don't understand how to convert it to fractions or rational numbers. Help me please!!!
 
Why? Just go with it as it stands.

[math]675^{1.6666666} = 675^{1\;2/3} = 675^{5/3}[/math]
They are the same. They all add the same. What does it matter?
 
Cuz I need to turn the entire number+exponent into either a fraction or a rational number
Mostly fractions.
 
vivia said:
I'm having a bit of problem with exponents. Not like [6[2], but more like[5[/6/97] or [675[/1.66666666666666666 (to infinity)]. Could someone help me? I just don't understand how to convert it to fractions or rational numbers. Help me please!!!
Click to expand...
Please try to use standard notation. I think you mean 6^2, 5^(6/97), and 675^1.6666... .

But what is it that you want to do? I'd just use a calculator. The latter two are not rational numbers, so you can't make them so!
 
vivia said:
Cuz I need to turn the entire number+exponent into either a fraction or a rational number
Mostly fractions.
Click to expand...
Since that isn't always possible (See Dr.Peterson's response), one must ask why you think this is a requirement for whatever it is you are doing. My guess is that you have not understood the assignment.
 
We're not allowed calculators, and I haven't misunderstood the assignment.
The requirement is to simplify these into a fraction.
Or a whole number
 
vivia said:
Actually you can, apparently.
I'll show you my assignment.
Click to expand...
Well, you can't turn the expressions you originally gave into rational numbers (that is, simplify them); but the actual problems are different. Things work better when you show what you really want. It will be even better when you show work and ask specific questions.

Each of these has its own specific trick. For example, #11 and others will be easier after you change the mixed number to an improper fraction. For #14, do that to both the base and the exponent. #16 and others just need the application of laws of exponents. Others need some factoring. Some look preposterous as they stand, but if you trust that they can be simplified, you'll be willing to try things you wouldn't otherwise bother with (such as hoping that some of the numbers have common factors, and dividing to find out).

Get to work, and let us know where you need specific help.
 
vivia said:
We're not allowed calculators, and I haven't misunderstood the assignment.
The requirement is to simplify these into a fraction.
Or a whole number
Click to expand...
You have misunderstood the assignment, perhaps only because the assignment isn't as clear as it should be.
 
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