Final answer:
\(\frac{5^9}{5^2}=5^7\) is the result of applying the law of exponents, which states that you subtract the lower exponent from the higher one when dividing like bases.
Step-by-step explanation:
The question \(\frac{5^9}{5^2}=5^?\) involves the rules for dividing powers with the same base. According to the mathematical laws of exponents, when you divide two powers that have the same base, you subtract the exponents. In this case, you have 5 raised to the power of 9 divided by 5 raised to the power of 2.
To find the answer, you will subtract the exponent of the denominator (2) from the exponent of the numerator (9), which gives you:
5^{9-2} = 5^7
So, the expression simplifies to 5^7. Using the concept of squares and other powers, we understand that an exponent is just shorthand for repeated multiplication. Thus, \(\frac{5^9}{5^2}\) equals 5^7, which is 5 multiplied by itself 7 times.