View Full Version : Exponents: Positive & Negative (simplify)

John Whitaker

06-06-2006, 08:55 AM

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

06-06-2006, 09:16 AM

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<sup>-1</sup>*x<sup>1</sup> = x<sup>0</sup> = 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<sup>-10</sup> in the numerator is equivalent to r<sup>10</sup> in the denominator

Thank you. John Whitaker

Denis

06-06-2006, 09:24 AM

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

06-06-2006, 10:56 AM

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

06-06-2006, 12:12 PM

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

06-06-2006, 12:24 PM

Denis.

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

John

skeeter

06-06-2006, 01:09 PM

x<sup>0</sup> = 1 for all values of x except x = 0 ... 0<sup>0</sup> is undefined.

\L

x \not= 0\quad \Rightarrow \quad 1 = \frac{{x^n }}{{x^n }} = x^{n - n} = x^0

John Whitaker

06-06-2006, 01:31 PM

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

06-06-2006, 01:35 PM

THICKNESS! THICKNESS!!!

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

John

skeeter

06-06-2006, 01:50 PM

THICKNESS! THICKNESS!!!

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

John

bingo

Denis

06-06-2006, 01:52 PM

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?

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