Exponents: Positive & Negative (simplify)

[John Whitaker]

The Problem: x^-3 x^2 r^-10 x / x^8 r^-2 r^-3 r^9
The Answer: 1 / 8^x r^14

Question #1: Combining like terms in the numerator, I get: x^-3 x^2, I get x^-1. How does the lone "x" at the end factor in?

Question #2: At what point do I know the answer will be a fraction with a 1 as the numerator?

Thank you. John Whitaker

 

[skeeter]

Re: EXPONENTS: Positive & Negative

The Problem: x^-3 x^2 r^-10 x / x^8 r^-2 r^-3 r^9
The Answer: 1 / 8^x r^14

Question #1: Combining like terms in the numerator, I get: x^-3 x^2, I get x^-1. How does the lone "x" at the end factor in?
x^-1*x¹ = x⁰ = 1

Question #2: At what point do I know the answer will be a fraction with a 1 as the numerator?
question 1 shows you what happens to the x's in the numerator ... r^-10 in the numerator is equivalent to r¹⁰ in the denominator

Thank you. John Whitaker

 

[Denis]

Hey, glad to see you're still "at it", John :idea:
x^-3 x^2 r^-10 x / x^8 r^-2 r^-3 r^9

Start with numerator; x by itself is same as x^1; add the powers:
x^-3 x^2 r^-10 x^1
= x^(-3+2+1) r^(-10)
= x^0 r^(-10)
= r^(-10)

Now the denominator:
x^8 r^-2 r^-3 r^9
= x^8 r^(-2-3+9)
= x^8 r^(4)

So we now have:
r^(-10) / (x^8 r^(4)) : can you finish it?

 

[John Whitaker]

Thank you Skeeter and Denis.
Yes, Denis, I'm still at it... doing pretty well too. I get stuck on some of the simplest things. But I am alone in this study and have nobody to bounce these things around with... except you, of course. I do appreciate the help, from everybody. Sure glad I found this site. John

 

[John Whitaker]

Denis,
I get it... except for one thing. RE: your 3rd line numerator. x^0. One of my lessons stated that a non-zero number raised to the zero power has a value of 1. It says nothing about a variable to the zero power. Can I conclude the rule does not apply to a variable?
John

 

[John Whitaker]

Denis.
Skeeter's reply indicates ^0 has a value of 1. No indication where this 1 is calclulated.
John

 

[skeeter]

x⁰ = 1 for all values of x except x = 0 ... 0⁰ is undefined.

 

[pka]

\(\displaystyle \L
x \not= 0\quad \Rightarrow \quad 1 = \frac{{x^n }}{{x^n }} = x^{n - n} = x^0\)

 

[John Whitaker]

Skeeter... thank you.
x^-3 x^2 r^-10 x is the numerator.
x^-3 x^2 = x^-1
But there is an additional "x" at the end of the numerator (past the "r^-10). This would seem to indicate:
x^-3 x^2 x^1 = x^0
If x^0 = 1, where does this "1" belong?
John

 

[John Whitaker]

THICKNESS! THICKNESS!!!
I think I got it the second after I sent the last. The "1" becomes the complete numerator... yes?
John

 

[skeeter]

THICKNESS! THICKNESS!!!
I think I got it the second after I sent the last. The "1" becomes the complete numerator... yes?
John

bingo

 

[Denis]

YES :idea:

"I think I got it the second after I sent the last." : that's Murphy's Law :wink:

example: 1 / 2 = 123456789123456789034^0 / 2 : ok?