Question

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

a. 4√x3
b. 1/(x^-1)
c. 10√x5•x4•x2
d. x^1/3* x^1/3* x^1/3

Answer 1

a.
`4\sqrt{x^(3)`

`4\sqrt{x^(2) * x}`

`4\sqrt{x^(2)}√(x)`

`4x√(x)`

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

c.
`10\sqrt{x^(5) * x^(4) * x^(2)}`

`10\sqrt{x^(11)`

`10\sqrt{x^(10)* x}`

`10\sqrt{x^(10)}√(x)`

`10x^(5)√(x)`

d.
`x^{(1)/(3)} * x^{(1)/(3)} * x^{(1)/(3)}`

`x`

The expressions that are equivalent are B and D.