Final answer:
To simplify 9 to the 4th power over 9 times the 10th power, you can subtract the exponents and rewrite it as 1/9^6.
Step-by-step explanation:
To simplify 9 to the 4th power over 9 times the 10th power, we can use properties of exponents. When we have a division of powers with the same base, we subtract the exponents. In this case, 9 to the 4th power divided by 9 to the 10th power is equal to 9^(4-10) = 9^(-6). To remove the negative exponent, we can rewrite it as 1/9^6. So, the simplified expression is 1/9^6.