Question

State the product law of exponents.

Answer 1

State the product law of exponents.

If  a  is any real number and  m,n are positive integers, then

 `a^m xx a^n = a^(m+n)`

By definition, we have

`a^m xx a^n = (a  xx a xx ...m " factor")   xx (a xx a xx ...n  "factor")`

`a^m xx  a^n = a xx a xx.....  "to " (m+n)` factors

`a^m xx a^n = a^(m+n)`

Thus the exponent "product rule" tells us that, when multiplying two powers that have the same base, we can add the exponents.