What is the quotient of 4^7 divided by 4^5?

To find the quotient of (4^7) divided by (4^5), you can use the properties of exponents. According to the quotient rule of exponents, when you divide two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator.

In this case, the base is 4. When dividing (4^7) by (4^5), you calculate:

[

4^7 \div 4^5 = 4^{7-5} = 4^2

]

This shows that the correct answer is (4^2).

Thus, when considering the choices, the correct one matches the result of the calculation. The quotient (4^2) correctly represents the simplified form of the division of (4^7) by (4^5), proving the mathematical operation follows the laws of exponents accurately.