Question

Which of the following are equivalent to 8/27?
A. 3^-3 * 2^3
B. (3/2) ^-3
C. 2^3/3^-3
D. (2^-3 * 3^3) ^-1

Answer 1

Note that when a number is raised to a negative exponent, we can make its exponent positive by getting its reciprocal.
Some examples:
2^-1 = 1/(2^1) = 1/2
3^-2 = 1/(3^2) = 1/9
2^-3 = 1/(2^3) = 1/8

Let's simplify each choice.
A.
3^-3 * 2^3
= ( 1/(3^3) ) * 2^3
= (1/27) * 8
= ?

B.
(3/2) ^-3
= (2/3)^3
= (2^3 / 3^3)
= ?

C.
2^3/3^-3
= 2^3 / (1/(3^3))
= 2^3 * 3^3
= ?

D.
(2^-3 * 3^3) ^-1
= 1 / (1/(2^3) * 3^3)
= ?

clue: there are three choices which are equivalent to 8/27. I think the problem asks for the one that isnot equivalent to 8/27?
hope this helps~ `u`