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5 votes
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

2 Answers

2 votes

Answer:

a) 3

Explanation:

243 = 3⁵

(243^-1/3)^-3/5 = (3⁵^-1/3)^-3/5

= 3⁻⁵/³*⁻³/⁵ = 3

User Vivek Sable
by
6.3k points
2 votes

Answer:

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.

User Thakis
by
6.7k points