Exponent Confusion for M Q Num Prop Bank

[caroline.welty]

Solution to DS q 8:

Value of (2^x + 2^x) / (s^y)

in solution one step goes from (2*(2^x)) / (2^y) --> (2^(x+1)) / (2^y)

What is the principle followed here?

Any thoughts?

[StaceyKoprince]

The formatting on here makes it hard to see what's going on, so you may want to follow this by writing it on a piece of paper yourself with normal symbology.

I'll strip out the denominator (2^y) because that doesn't change here

2*2^x = 2^1 * 2^x = 2^(x+1)

First, you can take any number and write it as itself raised to the 1 power.

Then, when the bases are the same, and the two terms are multiplied, you can combine them by adding the exponents (in this case 1 and x).

Make sense?