Multiplication Law

As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers.

           a^m × aⁿ  = a^m+n

Division Law

When two exponents having same bases and different powers are divided, then it results in base raised to the difference between the two powers.

          a^m ÷ aⁿ  = a^m / aⁿ  = a^m-n

Negative Exponent Law

Any base if has a negative power, then it results in reciprocal but with positive power or integer to the base.

            a^-m  = 1/a^m 

Rules of Exponents

The rules of exponents are followed by the laws. Let us have a look at them with a brief explanation.

Suppose ‘a’ & ‘b’ are the integers and ‘m’ & ‘n’ are the values for powers, then the rules for exponents and powers are given by:

i) a⁰ = 1

As per this rule, if the power of any integer is zero, then the resulted output will be unity or one.

Example: 5⁰ = 1

ii) (a^m)ⁿ = a(^mn)

‘a’ raised to the power ‘m’ raised to the power ‘n’ is equal to ‘a’ raised to the power product of ‘m’ and ‘n’.

Example: (5²)³ = 5^{2 x 3}

iii) a^m × b^m =(ab)^m

The product of ‘a’ raised to the power of ‘m’ and ‘b’ raised to the power ‘m’ is equal to the product of ‘a’ and ‘b’ whole raised to the power ‘m’.

Example: 5² × 6² =(5 x 6)²

iv) a^m/b^m = (a/b)^m

The division of ‘a’ raised to the power ‘m’ and ‘b’ raised to the power ‘m’ is equal to the division of ‘a’ by ‘b’ whole raised to the power ‘m’.

Example: 5²/6² = (5/6)²