Writing Quantities with a Common Base
We cannot multiply quantities if they do not have the same base. However, we can often
use the "power of a power" rule to write two quantities as quantities with a common base.
If the two bases are powers of a common base (for example, 4 and 32 are both powers of
2), rewrite each base as a power of the common base. Then uses the power of a power
rule to combine the exponents of each base. Finally, use the multiplication rule and add
the exponents.
Example: 95×274 =?
95 = (32)5 = 310; 274 = (33)4 = 312
95×274 = 310×312 = 310+12 = 322.
Summary of Properties
Addition: cxa + dxa = (c + d )xa
Subtraction: cxa - dxa = (c - d )xa
Multiplication: cxa×dxb = (cd )xa+b
Division: 
= (
)xa-b
Distribution: (cd )a = cada
Power of a Power: c(xa)b = cxab
