The product of powers tells us about that multiplying the powers with the same number you have simply have to add the exponents,
for example;
=6^3 * 6^3
=6^3 *6^3 (^3+^3) we are just adding the exponents even thou the operation is multiplication.
= 36^6
The power of power tells us about multiplying both the expression including the exponents. Power rule tells us that a power to a power, just multiply the exponents.
for example;
=6^3 * 6^3
=6^3 * 6^3 (^3*^3) we are multiplying both of the expression
=36^9