Exponents

Fractional exponents are defined as follows, . This permits manipulations with numbers with fractional exponents to be treated using the laws expressed earlier for integers. For example,

Summary

Pertinent information concerning exponents is summarized below.

Exponents Summary

Rule 1: To multiply numbers with the same base, add the exponents and keep the base the same.

Rule 2: When raising a power of a number to a power, multiply the exponents and keep the base the same.

Rule 3: When dividing two exponential numbers, subtract the powers.

Rule 4: Any exponential number divided by itself is equal to one.

Rule 5: To raise a product to a power, raise each factor to that power.

Rule 6: To raise a quotient to a power, raise both the numerator and denominator to that power.

Any number to the zero power equals one.

The rules for positive exponents apply to negative exponents. The rules for integer exponents apply to fractional exponents.