# 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:

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