Question

Jayne evaluated an expression that has a value of 1/729. Which expression could Jayne have evaluated? Check all that apply.

(-9)^3
9^-3
3^-6
(1/9)^-6
(1/3)^-6
(-3)^6

Answer 1

`(9)^(-3)`

`(3)^(-6)`

Explanation:

we have

`(1)/(729)`

Decompose the denominator in prime factors

`729=3^6`

substitute

`(1)/(729)=(1)/(3^6)=3^(-6)`

Verify each case

case 1) we have

`(-9)^3=-729`

`-729 \\eq (1)/(729)`

therefore

This expression could not have been evaluated by Jayne

case 2) we have

`(9)^(-3)=(1)/(9^(3))=(1)/(729)`

`(1)/(729)=(1)/(729)`

therefore

This expression could have been evaluated by Jayne

case 3) we have

`(3)^(-6)=(1)/(3^(6))=(1)/(729)`

`(1)/(729)=(1)/(729)`

therefore

This expression could have been evaluated by Jayne

case 4) we have

`((1)/(9))^(-6)=9^(6)=531,441`

`531,441 \\eq (1)/(729)`

therefore

This expression could not have been evaluated by Jayne

case 5) we have

`((1)/(3))^(-6)=3^(6)=729`

`729 \\eq (1)/(729)`

therefore

This expression could not have been evaluated by Jayne

case 6) we have

`(-3)^6=729`

`729 \\eq (1)/(729)`

therefore

This expression could not have been evaluated by Jayne

Answer 2

2 and 3

took the test