Question

243 whole power minus 1 by 5

Answer 1

Hello friends!!


Here is ur answer :


${(243)}^{ - \frac{ - 1}{5} }$


First we have to do the prime factorization of 243


$3 |243 \\ 3 |81 \\ 3 |27 \\ 3 |9 \\ 3 |3 \\ \: \: \: \: 1$



$243 = 3 \times 3 \times 3 \times 3 \times 3$


$243 = {3}^{5}$


So, we write 3^5 at the place of 243



$= { ({3}^{5}) }^{ \frac{ - 1}{5} }$


$= {(3)}^{5 \times \frac{ - 1}{5} }$


$= {3}^{ - 1}$


We know that,

${x}^{ - 1} = \frac{1}{x}$



$= > \frac{1}{3}$


HOPE IT HELPS YOU..

Answer 2

Hey there!

Given,

243 ^ ( -1/5)

= ( 3 * 81 ) ^ -1/5

= ( 3 * 3^4 ) ^ -1/5

= (3 ^5) ^ -1/5

= 3 ^ -5/5

= 3 ^ -1

= 1/3

Hope helped! ☺