Question

Which expressions have a value of 16/81? Check all that apply.

Answer 1

Answer: Which expressions have a value of StartFraction 16 Over 81 EndFraction? Check all that apply.

Best Option A, D

(A) <===== correct answer

(D) <===== correct answer

Explanation:

Answer 2

Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

Answer:

First and last option is correct.

`((2)/(3))^(4)=(16)/(81)`

`((4)/(9))^(2)=(16)/(81)`

Explanation:

Given:

There are four options.

(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

We need to check all given options for value of 16/81.

Solution:

Using rule.

`((a)/(b))^(n)=(a^(n))/(b^(n))`

Solve for option
`((2)/(3))^4`.

`((2)/(3))^(4)=(2^4)/(3^4)=(2* 2* 2* 2)/(3* 3* 3* 3)=(16)/(81)`

Solve for option
`((16)/(3))^4`.

`((16)/(3))^(4)=(16^4)/(3^4)=(16* 16* 16* 16)/(3* 3* 3* 3)=(65536)/(81)`

Solve for option
`((4)/(81))^2`.

`((4)/(81))^(2)=(4^2)/(81^2)=(4* 4)/(81* 81)=(16)/(6561)`

Solve for option
`((4)/(9))^2`.

`((4)/(9))^(2)=(4^2)/(9^2)=(4* 4)/(9* 9)=(16)/(81)`

Therefore, expression
`((2)/(3))^4` and
`((4)/(9))^2` have a value of
`(16)/(81)`.