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

Answer:

Option (a) is the correct answer.

Step-by-step explanation:

$[(243)^{-\frac{1}{3}}]^{-\frac{3}{5}$

We know that,

$(a^m)^n = a^{mn}$

Then,

$[(243)^{-\frac{1}{3}}]^{-\frac{3}{5}$

$=(243)^{(-\frac{1}{3})\times (-\frac{1}{5})$

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

$=(3\times3\times3\times3\times3)^{\frac{1}{5}$

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

Now, again using

$(a^m)^n = a^{mn}$

So,

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

Hence,

$[(243)^{-\frac{1}{3}}]^{-\frac{3}{5}}=3$

Therefore, option (a) is the correct answer.

Answer 2

Answer:

a) 3

Step-by-step explanation:

243 =  3⁵

(243^-1/3)^-3/5 = (3⁵^-1/3)^-3/5

         = 3⁻⁵/³*⁻³/⁵ = 3