Which of the folowing is the ascending order of `2^(1152), 3^(768), and 5^(384)`

Options

A. `5^(384), 3^(768), and 2^(1152)`
B. `5^(384), 2^(1152), and 3^(768)`
C. `5^(389), 5^(314), and 2^(1152)`
D. `2^(1152), 3^(768), and 5^(384)`

Answer

B

Explanation

Let us take GCD of `1152,768` , and 384 , which is 384.
`therefore 2^1152=(2^3)^384=8^384`
`3^768=(3^2)^384=9^(384)`
`5^384=(5)^384`
`therefore` The asceding order is as follows :
`5^384, 8^384, 9^384`
i.e., `5^384, 2^1152, and 3^768`
Hence, the correct option is (b).