Does the base change when you multiply and divide numbers that have the same base? Do the exponents change when you multiply and divide numbers with the same base? How?

Answer 1

When you multiply numbers with the same base, the base remains the same while the exponents are added together. For example, if you multiply 2^3 and 2^4, the result would be 2^(3+4) which is equal to 2^7.

Similarly, when you divide numbers with the same base, the base remains the same while the exponents are subtracted. For example, if you divide 2^5 by 2^3, the result would be 2^(5-3) which is equal to 2^2.

In summary, the base remains the same when you multiply and divide numbers with the same base, while the exponents are added and subtracted respectively.