Exponents and their rules

Fractional exponent is also called as a rational exponent which is in the form of a fraction like ½ (square root), ⅓ (cube root), ¼ (fourth root) etc.

A fractional exponent with 1/n is the n-th root of the given base.

(a)^ ⅓ = ³√a

A fractional exponent with m/n, we need to take the m-th power of the base and then find the n-th root or vice versa

(a) ^⅔ = ³√a²

The basic exponential rules are as follows: 

Exponents and tLaw of exponents:

1. Any number except zero when raised to zero equals 1
2. Any number raised to 1 equals itself
3. A number with negative power equals its reciprocal with a positive power
4. When we divide terms with same bases, the powers are subtracted
5. When we multiply terms with same bases, the powers are added
6. When a term is raised to a power with a whole power, the powers are multiplied.
7. When product of terms are raised to a power, each term is raised to that power

Subtracting exponents:

When we divide terms with same bases, the exponents are subtracted

The basic exponential rules are as follows: 

For example,

= 3³

Exponent rules:

1. When we multiply terms with same bases, the powers are added

2. When we divide terms with same bases, the powers are subtracted

3. Any number except zero when raised to zero equals 1

4. Any number raised to 1 equals itself

5. When a term is raised to a power with a whole power, the powers are multiplied.

6. When product of terms are raised to a power, each term is raised to that power

7. A number with negative power equals its reciprocal with a positive power