Add or multiply exponents

Power laws

The power laws allow us to group powers with similar properties, for example grouping powers with the same base or powers with the same exponent.

Multiplying powers by the same base

When multiplying powers with the same base, we add all the exponents and leave the base. Since this addition can also result in a negative number, we exclude zero for the base a. We call the exponents u and v.

Example:

Dividing powers by the same base

Dividing powers with the same base can be traced back to multiplying powers with the same base. Because dividing by a power is like multiplying by a power with a negative exponent.

Multiplying powers by the same exponent

Since the exponent u can be negative, we again have to exclude zero for a and b.

We can also do the math:

Dividing powers by the same exponent

Dividing powers by the same exponent works in the same way as multiplying.

We do the math:

Potentiating potencies