In most spoken contexts "степень" would be omitted, as in "десять в двадцать третьей". As for the thousandths, it is not so convenient with a zero after a decimal point, but usually just "и" is enough in informal speech:
1.6 * 10^-19 = один и шесть на десять в минус девятнадцатой.
It doesn't get shorter than that.
* I can only be sure as to how it is spoken amongst people grown accustomed to measurements, values, calculations and numbers in exponential form. Perhaps, "степень" should not be omitted in case you speak to a 12 year old.