Question

Which of the following expressions are equivalent? Justify your reasoning.

Answer 1

Working over the real numbers, expressions B and D are (almost) equivalent.

`(1)/(x^(-1)) = (1)/(1/x) = x`

`x^(\frac 1 3)x^(\frac 1 3)x^(\frac 1 3) = x^(\frac 1 3 + \frac 1 3 + \frac 1 3 ) = x`

They're not quite equivalent when x=0 as the first is undefined, but we'll let that go because we can't argue with the online system.

Answer: B and D

Answer 2

B )

x / x^-1 = x^1 = x

D)

x^1/3 * x^1/3 * x^1/3

= x^(1/3 + 1/3+ 1/3)

= x^3/3

= x^1

=x

Answer is B and D are equivalent