Problem 3

Explain why when different powers of the same quantity are multiplied together their exponents are added.

Solution. Consider and . By definition,

(multiply by itself times)

and

(multiply by itself times)

Their product is multiplied by itself times multiplied by multiplied by itself . Another words, multiplied by itself times

An alternative explanation uses logarithms:

and

and exponentiating both sides gives the same result.

Answer: