Final answer:
By applying the properties of exponents, the simplified expression of the problem 6^4 * 6^3 / 6^5 is 6^2, shown as option B.
Step-by-step explanation:
To approach this, we first need to remember the properties of exponents. According to the properties, when you multiply two numbers with the same base (in this case 6), you can add their exponents. Therefore, 6 to the power of 4 multiplied by 6 to the power of 3 is the same as 6 to the power of (4+3), which simplifies to 6 to the power of 7. Next, according to the properties of exponents, when you divide two numbers with the same base, you subtract their exponents. So, 6 to the power of 7 divided by 6 to the power of 5 simplifies to 6 to the power of (7-5), which simplifies to 6 to the power of 2. Therefore the simplified expression for the equation is 6 squared, which refers to option b, 6^2.
Learn more about Properties of Exponents