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# exponential functions [Solved!]

### My question

In expressions containing raised variables that are being divided, why do the variables not cancel each other out to a reciprocal of one? for example x^n/ x should be 1^n or is it still x^n?

### Relevant page

factoring polynomials with exponents - Google Search

### What I've done so far

(x^n/ x^n-2)^3 does this equal 1 or x^6?

X

In expressions containing raised variables that are being divided, why do the variables not cancel each other out to a reciprocal of one? for example x^n/ x should be 1^n or is it still x^n?
Relevant page

<a href="https://www.google.com/search?q=factoring+polynomials+with+exponents&oq=factoring+polynomials+with+exponents&aqs=chrome..69i57.14377j0j4&sourceid=chrome&ie=UTF-8">factoring polynomials with exponents - Google Search</a>

What I've done so far

(x^n/ x^n-2)^3 does this equal 1 or x^6?

## Re: exponential functions

Hello Sam

It's often best to try some real numbers in algebraic expressions first, to see what is going on.

Let's try 10^4.

This means 10 xx 10 xx 10 xx 10

If we divide this by 10, we would have

(10 xx 10 xx 10 xx 10)/10

We cancel one of the 10s on top with the 10 on bottom, to give:

10 xx 10 xx 10

So what we've done is

(10^4)/10 = 10^3

If you do this for several other indices, you'll hopefully conclude that:

(10^n)/10 = 10^(n-1)

In general, for your first question, we'd have:

x^n/ x = x^(n-1)

For your other question, (x^n/ x^n-2)^3, I'm not sure if you mean (x^n/ x^n-2)^3 or (x^n/ (x^n-2))^3?

You are encouraged to use the math entry system which makes it easier to express your questions and follow your working.

X

Hello Sam

It's often best to try some real numbers in algebraic expressions first, to see what is going on.

Let's try 10^4.

This means 10 xx 10 xx 10 xx 10

If we divide this by 10, we would have

(10 xx 10 xx 10 xx 10)/10

We cancel one of the 10s on top with the 10 on bottom, to give:

10 xx 10 xx 10

So what we've done is

(10^4)/10 = 10^3

If you do this for several other indices, you'll hopefully conclude that:

(10^n)/10 = 10^(n-1)

In general, for your first question, we'd have:

x^n/ x = x^(n-1)

For your other question, (x^n/ x^n-2)^3, I'm not sure if you mean (x^n/ x^n-2)^3 or (x^n/ (x^n-2))^3?

You are encouraged to use the <a href="http://www.intmath.com/forum/entering-math-graphs-images-41/how-to-enter-math:91">math entry system</a> which makes it easier to express your questions and follow your working.

## Re: exponential functions

Sam didn't reply.

If his second question meant (x^n/ x^n-2)^3, the the result is (1-2)^3=(-1)^3=-1

If he meant (x^n/ (x^n-2))^3, then there is no "nice" simplification.

X

Sam didn't reply.

If his second question meant (x^n/ x^n-2)^3, the the result is (1-2)^3=(-1)^3=-1

If he meant (x^n/ (x^n-2))^3, then there is no "nice" simplification.

## Reply

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