Exponents are operations. You know that removing a negative in the exponent means taking the reciprocal. Removing a whole number (like 4 = 4/1) in the exponent means repeated multiplication. This section adds another operation. The denominator in an exponent indicates a root.

Example 1

You should also be able to find the roots above without your calculator. You should also be able to do them on your calculator using your exponent key [y^x or ^]. Put parentheses around the exponent so that it all stays in the exponent.

When several operations are indicated in the exponent, do the root first. It's easier that way.

Remove 3 in the denominator,
Insert root,
Remove "-" in the exponent,
Take reciprocal,
and Remove power and multiply 4 times.

Summarizing:

All the exponent rules still work with fractional exponents. They are just messier.

Multiplying: Same base Keep base, add exponents:

Dividing: Same base Keep base, subtract exponents:

Power to a power: Keep base, multiply exponents:

Exponents distributed across a multiplication: