Final answer:
The student's questions involve simplifying expressions with exponents and the properties of multiplication of powers with the same base, which is to keep the base and add the exponents. The rules are demonstrated with the examples provided, including simplification and scientific notation.
Step-by-step explanation:
To answer the multiple parts of the student's question:
Examples that support the rules mentioned above:
The rule also applies in scientific notation and simplifies arithmetic significantly when dealing with powers of ten.