What identity is this? (Division to multiplication )

[musiclover55]

This isn't a homework help issue, I just want to know what identity(?) this is.

a/b to ab

or A^2/B^2 to (A^2)(B^2)

 

[Mark44]

This isn't a homework help issue, I just want to know what identity(?) this is.

a/b to ab

or A^2/B^2 to (A^2)(B^2)

There is no identity that converts a/b to ab, nor is there one to convert A²/B² to A²B².

What you might be thinking of is this one:

$$ \frac{a}{b} = a \cdot \frac{1}{b}$$

In other words, dividing by a number b is the same as multiplying by the reciprocal of b (1/b).

 

[LCKurtz]

What you might be thinking of is this one:

$$ \frac{a}{b} = a \cdot \frac{1}{b}$$

Or maybe this one:$$
\frac a {\frac 1 b} = ab$$

 

[rcgldr]

Although this probably isn't what you're looking for, there is a way to implement division or more specifically 1/b by iterating multiplications and additions via Newton Raphson method, but this seems unlikely to be what you're looking for.

For 1/b the iternation is:

x_i+1 = x_i (2 - b x_i)

This converges quadratically. For integers, usually a table of bytes is used to get the initial approximation.

 

[musiclover55]

Yea, thanks everyone. I thought that was possible, but obviously it's not lol.

 

[HallsofIvy]

Yet another possibility: A/B= AB^-1