1. ## Simplify this expression

Simplify: $(a^{-1}+b^{-2})^{-1}$

I know that's simple. I can express that as:

$\frac{1}{\frac{1}{a}+\frac{1}{b^{2}}}$

The problem is that, to me, that doesn't look any simpler.

I can't think of how else to express this. Is there another more appropriate answer?

2. Hi,
Originally Posted by jerry
Simplify: $(a^{-1}+b^{-2})^{-1}$

I know that's simple. I can express that as:

$\frac{1}{\frac{1}{a}+\frac{1}{b^{2}}}$

The problem is that, to me, that doesn't look any simpler.

I can't think of how else to express this. Is there another more appropriate answer?
You can just transform 1/a + 1/b² into a single fraction (common denominator), it depends on what you mean by "simple"

By the way, this is not an equation. An equation contains the = sign ! This is an expression ^^

3. Hello, jerry!

Simplify: . $(a^{-1}+b^{-2})^{-1}$

I can express that as: . $\frac{1}{\dfrac{1}{a}+\dfrac{1}{b^{2}}}$

The problem is that, to me, that doesn't look any simpler.

You have a complex fraction . . . one with more than two "levels".
. . We can and must simplify it further.

Multiply top and bottom by the LCD, $ab^2$

. . $\frac{{\color{blue}ab^2}\cdot(1)}{{\color{blue}ab^ 2}\cdot\left(\dfrac{1}{a}+\dfrac{1}{b^2}\right)} \;=\;\frac{ab^2}{b^2+a} \quad\hdots\quad see?$

4. OK. Thank you both for that!