Can I go any farther on these types of problems?

[cjcapta]

If I am correct, when dividing exponents you subtract them, do you still divide exponents if the exponent is 1? I have three problems, but they all call for the same answer: should I try subtracting the exponents or leave it be?
The directions say: Simplify each expression.
First question: p^(-1/5) My first answer: [p^(4/5)] / [p]
Second question: x^(-6/11) My second answer: [x^(5/11)] / [x]
Third question: [n^(1/3)] / [n^(1/6) * n^(1/2)] My third answer: [n^(2/3)] / [n]

 

[royhaas]

It isn't always clear what "simplifying" means. I would write, for example, \(\displaystyle p^{-1/5} = 1/p^{1/5}\).

 

[Loren]

Part of an answer depends on what is meant when the word "simplify" is used. Sometimes instructions call for the answer to be written with no negative exponents. Other times it may call for no fractional answers. For instance...

\(\displaystyle \frac{x^3}{x^5}\) can be simplified to x[sup:33eckod0]-2[/sup:33eckod0] or to \(\displaystyle \frac{1}{x^2}\) depending on the specific instructions.

 

[cjcapta]

I beleive now that I can't simplify it anymore. Our book, made by Glecoe, says it is simplified when no negative fractional exponents, no fractional exponents in denominator, no complex fractions, and the index of a radical must be the lowest it can possibly be.

 

[PAULK]

If I am correct, when dividing exponents you subtract them, do you still divide exponents if the exponent is 1? I have three problems, but they all call for the same answer: should I try subtracting the exponents or leave it be?
The directions say: Simplify each expression.
First question: p^(-1/5) My first answer: [p^(4/5)] / [p]
Second question: x^(-6/11) My second answer: [x^(5/11)] / [x]
Third question: [n^(1/3)] / [n^(1/6) * n^(1/2)] My third answer: [n^(2/3)] / [n]

My advice: Be careful how you speak (to yourself, of course). If you want to succeed in math, you must use the vocabulary correctly. When you write that:

3^4 = 81, for example,

3 is the base
4 is the exponent
81, the result, is the power.

Your rule says "When dividing POWERS of the same base, keep the base and subtract the exponents." Do not get lazy and start mixing up powers and exponents.

 

[mmm4444bot]

I beleive now that I can't simplify it anymore. Our book, made by Glecoe, says it is simplified when no negative fractional exponents, no fractional exponents in denominator, no complex fractions, and the index of a radical must be the lowest it can possibly be.

Hello CJ:

Using this Glecoe definition of simplification, all three of your posted answers are correct.

Cheers,

~ Mark

 

[cjcapta]

If I am correct, when dividing exponents you subtract them, do you still divide exponents if the exponent is 1? I have three problems, but they all call for the same answer: should I try subtracting the exponents or leave it be?
The directions say: Simplify each expression.
First question: p^(-1/5) My first answer: [p^(4/5)] / [p]
Second question: x^(-6/11) My second answer: [x^(5/11)] / [x]
Third question: [n^(1/3)] / [n^(1/6) * n^(1/2)] My third answer: [n^(2/3)] / [n]

My advice: Be careful how you speak (to yourself, of course). If you want to succeed in math, you must use the vocabulary correctly. When you write that:

3^4 = 81, for example,

3 is the base
4 is the exponent
81, the result, is the power.

Your rule says "When dividing POWERS of the same base, keep the base and subtract the exponents." Do not get lazy and start mixing up powers and exponents.

I'm not getting lazy, my teacher never taught me that. I beleive she's from Russia, so maybe that has something to do with it.