# Thread: Function Operations and Compositions

1. ## Function Operations and Compositions

The original equation is
11^(2/5)
11^(4/5)
I actually worked it to the point I got:
1
121^(1/5)
Can you show me or tell me how to solve this to where there is no rational # on bottom?

2. Originally Posted by runner940

The original equation is
11^(2/5)
11^(4/5)
I actually worked it to the point I got:
1
121^(1/5)

Can you show me or tell me how to solve this to where there is no rational # on bottom?

Multiply by $\frac{121^{\frac{4}{5}}}{121^{\frac{4}{5}}}$ (a cleverly disguised 1)

3. Originally Posted by runner940
The original [expression] is $\frac{11^{\frac{2}{5}}{11^{\frac{4}{5}}$.

I actually worked it to the point I got: $\frac{1}{121^{\frac{1}{5}}$.

Can you show me or tell me how to solve this to where there is no rational # on bottom?
Try using exponent rules:

. . . . . $\frac{x^m}{x^n}\, =\, x^{m\, -\, n}$

In your case, this means that the original expression simplifies as $11^{-\frac{2}{5}}\, =\, \frac{1}{(11^2)^{\frac{1}{5}}}$, as you mention.

Now you need to rationalize the radical denominator.

Hint: To be able to take the 121 out of the radical (the fifth root that is indicated by the one-fifth power), you need four more copies of 121 inside the root. So what should you multiply by?

Highlight the space below for a bigger hint.

$\huge\color{white}\frac{121^{\frac{4}{5}}}{121^{\f rac{4}{5}}}$