x^4/x^16

i don't know

12^10/12^2
12^8

5n^14/20n^7
i don't know

6^8/6^8
1

a^9b^5/a^3b^15
i don't know

/=divided by

x^4/x^16 = x^4/(x^4*x^12) = 1/x^12 = x^-12

5n^14/20n^7 = (5n^7*n^7)/(5*4*n^7) = n^7/4

a^9b^5/a^3b^15 = a^3a^6b^5/a^3b^5b^10 = a^6/b^10

not sure how you got some and had no idea on others which were very similar.

thanks!!

To simplify the expressions involving division of exponents, we can apply the properties of exponents. Specifically, we can subtract the exponents when dividing variables with the same base.

Let's go through the given expressions one by one:

1. x^4 / x^16:
To divide exponents with the same base, subtract the exponents. In this case, we have x^4 divided by x^16. This can be simplified as x^(4-16), which simplifies to x^(-12). Therefore, the answer is 1 / x^12.

2. 12^10 / 12^2:
Since both terms have the same base (12), we can subtract the exponents. In this case, we have 12^10 divided by 12^2. This simplifies to 12^(10-2), which simplifies to 12^8. Therefore, the answer is 12^8.

3. 5n^14 / 20n^7:
To divide exponents with the same base, subtract the exponents. In this case, we have 5n^14 divided by 20n^7. The constant term 5 divides by 20 to give 1/4, and the variable term n^14 divides by n^7, resulting in n^(14-7), which simplifies to n^7. Therefore, the answer is (1/4)n^7.

4. 6^8 / 6^8:
Since both terms have the same base (6), we can subtract the exponents. In this case, we have 6^8 divided by 6^8. This simplifies to 6^(8-8), which simplifies to 6^0. Any number raised to the power of 0 equals 1. Therefore, the answer is 1.

5. a^9b^5 / a^3b^15:
To divide exponents with the same base, subtract the exponents. In this case, we have a^9b^5 divided by a^3b^15. This results in a^(9-3) times b^(5-15), which simplifies to a^6 times b^(-10). Therefore, the answer is a^6 / b^10.

Remember, when dividing exponents with the same base, subtract the exponents. And if an exponent is negative, move the base to the denominator.

Hope that helps! If you have any further questions, feel free to ask.