what is multiplication proprties of exponents?

Answer 1

Since you didn't really clarify your particular concern, there are TWO processes that you might have been asking about:

1. a^p times a^q = a^(p + q); and

2 (a^s)^t = a^(st).

Those are the two facts you need to work out any product or multiple power of anything.

CHECKING THE ABOVE SUMMARIES

You can easily check these two relationships out for yourself by letting a = 10, p = 2, q = 3, s = 2, and t = 3, and then simply counting out the zero's in the following "powers of 10" examples. Using the cases 1 and 2 from above :

1: (10^2) x (10^3) = 100 x 1,000 = 100,000 = 10^5.

(See how the exponents ADDED.)

2: (10^2)^3 = 100^3 = 1,000,000 = 10^6.

(See how the exponents MULTIPLIED, this time.)

Live long and prosper.

Answer 2

When you multiply exponents with the same base, then you simply add the exponents.

Answer 3

if you are multiplying quantities with an exponent, use this rule: (x^n)(x^m)=x^(n+m)
example: (x^2)(x^1)=x^3

if you are putting a quantity to an exponent, follow this rule:
(x^n)^m= x^(nm)
example: (x^2)^3= x^6