Question

Simplify the expression. 216^5/6
I keep getting 2^5/2 * 3^5/2 but these are the only answer choices.
6
36 sqrt 6
6^5sqrt6
180

Answer 1

I got C
what are the factors of 216= 2*2*2*3*3*3
can be expressed as 6*6*6 = 6^3
when you raise a power to a power multiply the powers and sqrt = power 1/2
apply to this problem
216^5/6 = 6^3*(5/6) = 6^5/2 = 6^5sqrt6

Answer 2

by the way your answer is correct
a^n *b^n = (ab)^n
you have 2^5/2 * 3^5/2 = (2*3)^5/2 = 6^5/2

Answer 3

Thank you so much!