Final answer:
To find the quotient of (8^3x+1) * (2^x), you need to simplify the expression using the rule that states when multiplying two numbers with the same base, you add the exponents. The final quotient is 2^(13x+3).
Step-by-step explanation:
To find the quotient of (8^3x+1) * (2^x), you need to simplify the expression. Start by using the rule that states when multiplying two numbers with the same base, you add the exponents.
So in this case, the exponents 3x+1 and x are added together, resulting in 4x+1. The base remains the same, which is 8^4x+1 * 2^x.
Next, you can simplify the expression further by multiplying the pre-factors. In this case, 8^4x+1 can be written as (2^3)^4x+1, which is equal to 2^12x+3.
Now you have 2^12x+3 * 2^x, which can be simplified using the same rule as before: add the exponents. So the final quotient is 2^(12x+3+x), which simplifies to 2^(13x+3).