Which statement is true?
A. 6^18/6^5 < (6^4)^2
B. 6^18/6^5 > (6^4)^2
C. 6^18/6^5 = (6^4)^2
A. 6^18/6^5 < (6^4)^2
AAAaannndd the bot gets it wrong yet again!
(6^4)^2 = 6^8
6^18/6^5 = 6^13 > 6^8
I apologize for the confusion. You are correct, the answer is B. 6^18/6^5 > (6^4)^2.
To determine which statement is true, let's simplify each side of the inequality and then compare them.
Statement A: 6^18/6^5 < (6^4)^2
To simplify the left side, we can subtract the exponents: 6^(18-5) = 6^13
To simplify the right side, we can calculate the exponent: (6^4)^2 = 6^8
So, statement A becomes 6^13 < 6^8.
Statement B: 6^18/6^5 > (6^4)^2
Again, simplifying the left side, we have 6^(18-5) = 6^13.
The right side remains the same as in statement A: (6^4)^2 = 6^8.
Therefore, statement B becomes 6^13 > 6^8.
Statement C: 6^18/6^5 = (6^4)^2
The left side again simplifies to 6^(18-5) = 6^13.
The right side remains the same as in statement A and B: (6^4)^2 = 6^8.
Hence, statement C becomes 6^13 = 6^8.
Now let's compare the three statements:
- Statement A: 6^13 < 6^8
- Statement B: 6^13 > 6^8
- Statement C: 6^13 = 6^8
Looking at the exponents, we can see that 6^13 is not equal to 6^8. When the exponents are different, the number with the larger exponent will be bigger. Therefore, statement A is false.
Comparing statement B and C, we see that 6^13 cannot be both greater than and equal to 6^8. Hence, only one of them can be true. To determine which one is true, we can calculate the values of 6^13 and 6^8.
Using a calculator or mathematical software, we find that 6^13 ≈ 13060694016 and 6^8 = 1679616. Hence, 6^13 is indeed greater than 6^8.
Therefore, the correct answer is:
B. 6^18/6^5 > (6^4)^2