The Law of Exponents or Index Laws enable us to simplify calculations using powers.  When working with normal calculations, the base will be 10, so it serves to just consider these laws with respect to base 10.

For Multiplication:

When multiplying powers of ten, the answer's exponent is the sum of the exponents of the factors.

For Division:

When dividing powers of ten, the answer's exponent is the difference between the numerator's exponent and the denominator's exponent.

 

We shall use these laws for estimating the results to some of our problems.