DzaWeb: Negative Indices, Zero Indices and Exponents that are Fractions:

Negative Indices:

So far we have worked with positive exponents or indices. You remember from the Division Law of Indices that:

a³ ÷ a⁵ = a^{3 – 5}= a^-2 and that:

Fraction Raised to Negative Whole Exponent

Example:

Simplify the following.

Zero Indices:

Note that for any number a, except for a = 0. [thus whether a is a whole number, fraction or decimal], the rule still holds.

Complete these examples.

Simplify the following:

1. 3^{n – 1}× 3^{1
– n}

2. 3^x × 3^-x

3. (2a²)³ × 3a^-6

Exponents that are Fractions:

This means that you must look for the number that when multiplied by itself four times gives 16. It is written as

This is called the fourth root of 16.

Generally,

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