how to express a number only in exponential form of product of 3 and 7 or say any two numbers?

Question

please guide me how to expand a number in the form of $3^x 7^y$ example:

$1 = 3^0 7^0$

$21 = 3^1 7^1$

i have tried by finding numbers which can be expressed in form of any one such as for only $3^x$ but cant find in the product form

Answer 1

You need to factorise the number into prime dividers. Then, look for the number of 3's and the number of 7's and that are the exponents of 3 x 7 y