Laws of Exponents

The same laws hold for rational-number exponents as for integer exponents.

We list them for review.
For any real number a and any rational exponents m and n:

1. In multiplying, we can add exponents if the bases are the same.

2. In dividing, we can subtract exponents if the bases are the same.

3. To raise a power to a power, we can multiply the exponents.

4. To raise a product to a power, we can raise each factor to the power.

5. To raise a quotient to a power, we can raise both the numerator and the denominator to the power.

Provide an example of two of the laws of exponents. Explain how to simplify them. Tell how do the laws work with rational exponents and then provide a third example to simplify that includes a rational (fractional) exponent.