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.

$\dfrac{1}{x^{-1}} = \dfrac{1}{1/x} = x$

$x^{\frac 1 3}x^{\frac 1 3}x^{\frac 1 3} = x^{\frac 1 3 + \frac 1 3 + \frac 1 3 } = x$

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