# Thread: Simplify Expression for y

1. ## Simplify Expression for y

Simplify for y.

I have to simplify what y equals to.

y = 1 divided by n(x^[(1/n)(n - 1)]

Everything in red is the exponent of x.

How do I simplify what y equals to?

2. Originally Posted by sharkman
Simplify for y.

I have to simplify what y equals to.

y = 1 divided by n(x^[(1/n)(n - 1)]

Everything in red is the exponent of x.

How do I simplify what y equals to?
Multiply out the factors in the exponent of x. That will simplify the exponent. Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?

3. ## ok...but

Originally Posted by QM deFuturo
Multiply out the factors in the exponent of x. That will simplify the exponent. Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?
In the numerator, we have (1/n)(n - 1).

(1/n)(n - 1) = (n - 1)/n...This is the new exponent.

You also said:

"Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?"

Can you show me the rest of the way?

4. Originally Posted by sharkman
In the numerator, we have (1/n)(n - 1).

(1/n)(n - 1) = (n - 1)/n...This is the new exponent.

You also said:

"Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?"

Can you show me the rest of the way?

Remember that $\frac{1}{a^b} = \frac{a^{-b}}{1}$

5. ## then...

Originally Posted by QM deFuturo
Remember that $\frac{1}{a^b} = \frac{a^{-b}}{1}$
I'll have to play with this one some more.

6. I will take the equation to be as follows:

. . . . . $y\, =\, \frac{1}{nx^{\left(\frac{1}{n}\right)(n\, -\, 1)}}$

If so, then note that (1/n)(n - 1) = -(1/n)(1 - n), and negative exponents mean to move the base to the other side of the fraction line, so we get:

. . . . . $y\, =\, \frac{x^{\left(\frac{1}{n}\right)(1\, -\, n)}}{n}$

I'm not sure that anything "simplifies" much after this point....

7. Originally Posted by stapel

$y\, =\, \frac{x^{\left(\frac{1}{n}\right)(1\, -\, n)}}{n}$

I'm not sure that anything "simplifies" much after this point....
Well, not much. But you could do :

$(\frac{1}{n})(1 - n) = (\frac{1}{n} - 1 )$

That's slightly simpler

8. ## ok....

Originally Posted by QM deFuturo
Well, not much. But you could do :

$(\frac{1}{n})(1 - n) = (\frac{1}{n} - 1 )$

That's slightly simpler
Yes, that is as simple as it gets.