Understanding Exponent Multiplication: cnxn-1

[PhysicsBoyMan]

Homework Statement

x(cnx^n-1)

3. The Attempt at a Solution

I know that the answer is cnxⁿ

I'm not sure why though. My thinking is that we have cnx^n-1 and we multiply that by x. x times x is x² so I'm expecting a 2 to interact with the n-1 in the exponents. I'm just not sure how n-1 interacts with 2 to produce n.

I don't add n-1 + 2 to get n + 1 because I already have the answer and its not that. I just can't see how I would get from n-1 to n by interacting with a 2.

Thanks for the help.

 

[SammyS]

Homework Statement

x(cnx^n-1)

3. The Attempt at a Solution

I know that the answer is cnxⁿ

I'm not sure why though. My thinking is that we have cnx^n-1 and we multiply that by x. x times x is x² so I'm expecting a 2 to interact with the n-1 in the exponents. I'm just not sure how n-1 interacts with 2 to produce n.

I don't add n-1 + 2 to get n + 1 because I already have the answer and its not that. I just can't see how I would get from n-1 to n by interacting with a 2.

Thanks for the help.

You may know the answer to the question.

We're not any good at guessing just what that question might be.

What is the question?

 

[PhysicsBoyMan]

The question is the multiplication of x times cnx^n-1

 

[SteamKing]

Homework Statement

x(cnx^n-1)

3. The Attempt at a Solution

I know that the answer is cnxⁿ

I'm not sure why though. My thinking is that we have cnx^n-1 and we multiply that by x. x times x is x² so I'm expecting a 2 to interact with the n-1 in the exponents. I'm just not sure how n-1 interacts with 2 to produce n.

I don't know where you are getting that you are multiplying x times x here.

You are multiplying x times x^n-1, which is something different.

That's what x(cnx^n-1) means. It can also be written as c ⋅ n ⋅ x ⋅ x^n-1

 

[SammyS]

The question is the multiplication of x times cnx^n-1

Oh! You want to simplify the product, x⋅cnx^n-1 .

So the 'question' is:

What is the result of simplifying x⋅cnx^n-1 ?
​

And you want to know how it is that simplifies to be cnxⁿ .
.

 

[HallsofIvy]

Have you never actually taken an Algebra class? If you have you should have learned one of the basic 'laws of exponents':
(a^m)(a^n)= a^{m+n}. Here the problem is to multiply x, which is the same as x^1, by x^{n-1}.
Mod note: Portion deleted as too much help.