Which of the following expressions have values are less than the expression below?
6^14 divided by 6^2.
A. 6^8 divided by 6^-6
B. (6^3)^3
C. 6^15 x 6^-2
D. 6^9 divided by 6^-2
E. 6^16 x 6^-4
To simplify the expression 6^14 divided by 6^2, we subtract the exponents:
6^14 divided by 6^2 = 6^(14-2) = 6^12
Now, we can compare the expressions:
A. 6^8 divided by 6^-6 = 6^(8+6) = 6^14
Since A = 6^14, A is greater than 6^12.
B. (6^3)^3 = 6^(3*3) = 6^9
Since B = 6^9, B is less than 6^12.
C. 6^15 x 6^-2 = 6^(15-2) = 6^13
Since C = 6^13, C is less than 6^12.
D. 6^9 divided by 6^-2 = 6^(9+2) = 6^11
Since D = 6^11, D is less than 6^12.
E. 6^16 x 6^-4 = 6^(16-4) = 6^12
Since E = 6^12, E is equal to 6^12.
Therefore, the expressions that have values less than 6^14 divided by 6^2 are B (6^9) and D (6^11).