Final answer:
When multiplying two powers with the same base, you add the exponents, so 6³ * 6´ = 6·. The number of factors of 6· would require prime factorization and is not directly answered by the exponentiation.
Step-by-step explanation:
The student is asking how to multiply two powers of the same base, specifically, to multiply 6³ by 6´. According to the laws of exponents, when multiplying two powers that have the same base, you add the exponents. So 6³ * 6´ is equal to 6·, since 3 + 4 = 7.
This is similar to other exponentiations, such as (5³)*, which is 5 multiplied by itself 3 times, 4 times over, resulting in 5 raised to the 12th power, or (5³ * 5´ = 5·).
Additionally, when discussing how many factors a certain number - in this case, 6· - has, it's important to understand the concept of factors or divisors of a number. To find out how many factors a number has, you would need to prime factorize that number and use the exponents of its prime factors in a specific formula.
However, for the power of a single number as in this question, the number of factors is not directly related to the exponent itself and would require a further specific calculation of the prime factors of 6·.