Question

Evaluate (243^-1/3)^-3/5

a.
3
c.
27
b.
–3
d.
–27


Please select the best answer from the choices provided

A
B
C
D

Answer 1

a) 3

Explanation:

243 = 3⁵

(243^-1/3)^-3/5 = (3⁵^-1/3)^-3/5

= 3⁻⁵/³*⁻³/⁵ = 3

Answer 2

Option (a) is the correct answer.

Explanation:

`[(243)^{-(1)/(3)}]^{-(3)/(5)`

We know that,

`(a^m)^n = a^(mn)`

Then,

`[(243)^{-(1)/(3)}]^{-(3)/(5)`

`=(243)^{(-(1)/(3))* (-(1)/(5))`

`=(243)^{(1)/(5)`

`=(3*3*3*3*3)^{(1)/(5)`

`=(3^5)^{(1)/(5)`

Now, again using

`(a^m)^n = a^(mn)`

So,

`(3^5)^{(1)/(5)}=3^{5*(1)/(5)}=3^1=3`

Hence,

`[(243)^{-(1)/(3)}]^{-(3)/(5)}=3`

Therefore, option (a) is the correct answer.